"They were in with loads of opt-outs, now they are out and want a load of opt-ins."

Luxembourg Prime Minister Xavier Bettel's pithy description back in March of the U.K.'s approach to the Brexit talks is looking even more apt now that negotiators have finally gotten around to talking about what the future relationship will actually look like.

The full extent of those opt-ins (or at least the ones the U.K. would like to negotiate) is starting to become clear and it seems Britain is quite keen on many aspects of the EU after all.

Will the EU allow such cherry-picking? The U.K.'s argument in each case is that allowing it to remain part of Continent-wide arrangements on say, airline safety and medicines regulation, is the most sensible way forward.

But so far, Barnier has rebuffed the Brits. He underscored his position in a speech last month in Estoril, Portugal: "The United Kingdom wants to leave. That is its decision. Not ours. And that has consequences."

London hopes this tough talk is an opening negotiating position that will morph into something more pragmatic once discussions on the U.K.'s future relationship really hit their stride. (Negotiators only began scoping out topics for those talks at the beginning of May, and little progress has been made since.)

POLITICO has a guide to all the bits of the EU that Britain wants in its post-Brexit world:

Galileo satellite program

Theresa May's Cabinet doesn't agree on much when it comes to Brexit, but Remainers and Leavers are united in their exasperation with the EU over Galileo. Britain has ponied up €1.2 billion for developing the satellite navigation system. It views the EU's threat of excluding the country from the high-level, military-grade part of the program as legalistic at best and deliberately hostile at worst.

The U.K. — which ironically tried to block the Galileo project when it was first conceived — is so annoyed that it is now threatening to build its own. “We need access to a satellite system of this kind," Chancellor Philip Hammond told journalists in Brussels last month. If the EU freezes out the U.K., he added, "Britain will have to go it alone, possibly with other partners outside Europe and the U.S., to build a ... competing system."

The EU's refusal to reimburse the money Britain has spent on the program just makes it harder for London to take.

Scientific research

Even some of the most ardent Brexiteers love the EU's science program, and it's easy to see why. The U.K. is a dominant player in European research, winning 15 percent of the funding and applying for more projects than any other EU country. The U.K. now gets £1.24 back for every pound it puts into the funding pot and being part of EU science means opportunities for collaboration across the Continent.

In its pitch on science, the U.K. said it will seek "full association" with Horizon Europe, the EU's €98 billion science program, and will be happy to make a "fair contribution" to its costs. But negotiators want greater influence on decision-making than any other non-EU country. "As an associate country we would look to agree an appropriate level of influence on the shape of the programme. This should be greater than current non-EU precedents, recognising the quality and breadth of the UK’s contribution."

In other words: We're special and we'd like to keep things very much as they are.

Erasmus

Who would want to step away from a program that will provide study opportunities abroad for some 2 million young people during the current budget period, as well as boosting volunteering, employment training, entrepreneurship and sport?

Certainly not the U.K. government — despite Brexit.

"Erasmus is one of the institutions that we may stay a member of, if we can negotiate that, after we leave," Brexit Secretary David Davis said in the House of Commons in November.

Davis may just be in luck. In its proposal for its new multiyear budget post 2020, the European Commission is proposing opening the program up to any country that agrees to a "fair balance" of contributions and benefits. In other words: Pay up and you can join in.

Security and terrorism

The U.K. participates in more than 40 EU measures covering police and judicial cooperation in criminal matters, according to the government. London says that for many of these schemes, such as the European Criminal Records Information System, Europol and Passenger Name Records, the precedent for third-country involvement either doesn't exist or is inadequate.

Take the European Arrest Warrant: For every person arrested on a U.K.-issued warrant, Britain arrests eight people on warrants issued by EU27 countries. Since 2004, the U.K. has surrendered more than 10,000 people under the scheme.

The U.K. wants to negotiate a new treaty that would keep things much the same as they are now. However, agencies like Europol operate under the jurisdiction of the European Court of Justice — and May had set leaving the ECJ as a red line in the talks, although her Mansion House speech indicated a softening on that point.

Medicines

One of the first impacts of Brexit will be the European Medicines Agency, with its 890 full-time staff and 36,000 experts attending scientific meetings each year, moving from London to Amsterdam.

The U.K. is powerless to prevent it, but doesn't want to be outside the EMA's system of regulating medicines altogether. In her Mansion House speech, May said: "We will also want to explore with the EU the terms on which the U.K. could remain part of EU agencies such as those that are critical for the chemicals, medicines and aerospace industries: the European Medicines Agency, the European Chemicals Agency, and the European Aviation Safety Agency. We would, of course, accept that this would mean abiding by the rules of those agencies and making an appropriate financial contribution."

Whitehall fears the U.K. will become less of a priority for pharmaceutical companies, who will concentrate first on getting products licensed in the much larger EU market. U.K. patients could have to wait longer for the latest life-saving drugs, and the need for a parallel regulatory system could increase drug prices, too.

Aviation

Grounded planes, ruined holidays and missing international business meetings would be a disastrous way to embark on Brexit. Aviation safety is one area where there is no real advantage to diverging from EU rules, so London would like to keep things much as they are. After meeting industry representatives last month, Brexit Minister Steve Baker said: "We are focused on reaching an agreement with the EU which secures the right arrangements for this vital industry."

The government wants to remain part of the European Aviation Safety Agency. And, unlike other sectors of the economy, aviation cannot fall back on World Trade Organization rules to keep operating. Rights to fly between countries and embark and disembark passengers and freight are based on ownership percentages (at least 50 percent EU ownership for EU airlines), so some alternative needs to created.

For its part, the EU has said it will negotiate a bilateral aviation safety agreement but that future membership of EASA is not possible.

Chemicals

British chemical producers have been vocal in protesting Brexit, and for good reason: They have a lot to lose. The European Chemicals Agency (ECHA) owns and maintains the world’s most comprehensive database on chemicals: If the U.K. is no longer part of the agency, deciding who owns the data submitted by British companies would be messy (especially as registrations are often shared between companies across the bloc that produce the same chemical).

That's not all: Without complying with the EU’s chemical regulation REACH, producers will not be able to access the EU market. The EU is constantly updating its lists of banned and restricted chemicals, so the two regimes will diverge unless the U.K. regularly copies ECHA’s decisions on individual chemicals. That may not sound much like the Brexiteer narrative of taking back control, but anything less means producers who want to export to the EU must comply with two sets of rules, increasing red tape and costs.

May floated has "associate membership" of the ECHA, but it's unclear whether the EU will allow that.

Energy

May told her Mansion House audience that the U.K. wants "to secure broad energy cooperation with the EU." That would include maintaining the single electricity market that operates on the island of Ireland "and exploring options for the U.K.’s continued participation in the EU’s internal energy market."

But Brexit will almost certainly mean one concrete change: The U.K. will leave the atomic energy community Euratom. That poses some significant problems. The 60-year-old Euratom pre-dates the EU and, among other things, makes sure countries don’t use their nuclear materials for weapons, manages nuclear fuel supply, allows workers and equipment to move freely, and funds research and innovation.

Those are crucial functions for the U.K., home to the world’s biggest stockpile of civil plutonium and 15 nuclear reactors made up of parts sent from EU members and countries that have nuclear cooperation agreements with Euratom. Without a replacement agreement, the U.K. will run out of nuclear fuel and cancer patients will cease to have access to specialized radionuclides that are used in their care.

Financial services

In 2017, the financial services sector contributed £119 billion to the U.K. economy (6.5 percent of total economic output) and supported 1.1 million jobs, according to figures from the House of Commons Library. It also makes up a big chunk of the U.K. government's tax base (£27.3 billion in 2016-17). That's more than the expenditure by the Home Office, the Department for International Development and the Foreign Office combined.

Being outside the EU poses problems: London has accepted that businesses based in the U.K. will lose their passport to operate across the EU, but it does not want to settle for the status normally reserved for countries outside the bloc — so-called equivalence.

In a speech in March, U.K. Chancellor Philip Hammond said equivalence is “wholly inadequate for the scale and complexity of the U.K.-EU financial services trade.” Plus, Brussels could decide to withdraw equivalence with very little notice if it thinks the U.K.'s rules have diverged too much.

The U.K. wants financial services to be part of a "comprehensive economic partnership" guaranteeing market access to businesses and consumers in the U.K. and EU, it argued last month.

Broadcasting

U.K. companies provide around 30 percent of the television channels across the EU while 35 channels and on-demand services offered in the U.K. are licensed in EU27 countries. With British creative industries worth around £92 billion annually, the government does not want to lose access to the EU market.

May has acknowledged that the rules allowing a broadcasting company licensed by U.K. regulator Ofcom to broadcast across the EU will cease to apply to the U.K. But she argued that EU27 citizens would hate to miss out on British shows.

Data protection

U.K. Digital Secretary Matt Hancock is almost evangelical in his praise of the EU's new data rule — the General Data Protection Regulation. When GDPR came into force last month, he tweeted jovially: “I’m enjoying spending my Wednesday morning drafting my Privacy consent email for my newsletters. Coming to an inbox near you… #GDPR."

Hancock knows there is a lot at stake. The value of the European data economy is set to increase to €739 billion by 2020 (4 percent of overall GDP), according to some estimates, and EU exports to the U.K. of data-reliant services were worth approximately €36 billion in 2016, in sectors as diverse as finance, telecoms and entertainment. The government wants to keep that data flowing after Brexit to avoid disruptions for businesses and public services — and to maintain data sharing by security services.

London's pitch is for recognition that U.K. laws and regulations provide data protection standards that are essentially equivalent to those applied in the EU. According to a document setting out the government's negotiating aims, ministers want to go even further than the so-called adequacy approach for third countries, to create a uniquely close arrangement.

Frictionless trade

The U.K.'s future trading relationship is fundamental to what kind of Brexit emerges. The British government has been clear for months about what it doesn't want — membership in the EU single market and the customs union. The former would mean accepting freedom of movement, something the government calculates was a major driver for Brexit voters, and remaining in the latter would hinder the U.K.'s ability to do trade deals with countries around the world.

But those aside, the government gives the impression of wanting to keep things as close to the status quo as possible. "I want the broadest and deepest possible partnership — covering more sectors and cooperating more fully than any free-trade agreement anywhere in the world today," May said in the Mansion House speech.

Her government will consider sticking with EU state aid rules and its competition regime, but further binding commitments would be in return for "commensurate levels of market access."

May's five pillars for a close future economic relationship are: commitments to ensure fair and open competition; an independent arbitration mechanism; an ongoing dialogue with the Brussels; data-protection arrangements; and maintaining the links between "our people."

To many in EU, that sounds a lot like staying in the club.