A day after parliament voted overwhelmingly to give Theresa May the power to trigger article 50, the government presented MPs with its formal policy paper setting out how the UK proposes to leave the EU.

Here are the key points of the Brexit white paper, which essentially builds and expands on May’s Lancaster House speech last month. It amounts to a list of objectives, many of which will not necessarily be easy to achieve.

Sovereignty, great repeal bill and control of UK laws

The paper says the British parliament has been sovereign throughout the UK’s EU membership, “but it has not always felt like that” – a striking comment.

It says the government will bring forward a separate white paper on the great repeal bill, which was first announced by May in her Conservative party conference speech last year to remove the European Communities Act of 1972 from the UK statute book and convert the body of existing EU law into domestic law.

The paper confirms that “wherever practical and appropriate” the same rules and laws will apply in the UK on the day after it leaves the EU as did before.

It also confirms that the government intends to “take control of our own laws”, which will mean “bringing to an end the jurisdiction of the European court of justice in the UK” and establishing a new mechanism for resolving future disputes between the UK and the EU.

The union and Ireland

The paper says the government will “work with the devolved administrations on an approach to returning powers from the EU that works for the whole of the UK and reflects the interests of Scotland, Northern Ireland and Wales” but does not go into specifics.

It also promises that no decisions currently taken by the devolved administrations will be taken away from them, and indeed that more decisions will be devolved (it does not say which). And it says it will pay particular attention to the Isle of Man, Channel Islands and Gibraltar, all of which have unique relationships with the EU.

On the island of Ireland and the common travel area with the UK, the paper notes the UK and Irish economies are “deeply integrated” and says the government will work to “develop and strengthen” those ties after Brexit.

It says it aims to retain “as seamless and frictionless a border as possible” between Northern Ireland and the Republic, and wants Irish and UK citizens to be able to continue to move freely north-south and east-west, “while protecting the integrity of the UK’s immigration system”. Again, it does not say how.

Immigration and reciprocal citizens’ rights

On the rights of EU nationals living in the UK and vice versa, the white paper goes no further than May’s speech.

It says securing their status is “one of this government’s early priorities for the forthcoming negotiations” and reiterates that “the UK remains ready to give people the certainty they want … at the earliest opportunity”. (The EU-27 have always seen this as part of article 50 negotiations).

It says it is consulting with expatriate groups abroad and EU businesses and other groups “to ensure we understand their priorities”, and “recognises the priority placed on easy access to healthcare by UK nationals living in the EU” – a key concern of many, particularly pensioners.

On controlling immigration, the paper offers no clarity. It says the government is “considering very carefully” the options open to it and working to “understand the impacts on the different sectors of the economy and the labour market”.

Businesses and communities will be able to contribute their views, it says, and suggests – for the first time with regard to immigration – that “there may be a phased process of implementation”, to give companies and individuals time to plan and prepare.

It says EU students can continue to come and study, in the short term at least, but says nothing about future access for EU workers. It also says workers’ rights under EU law will be preserved after Brexit.

EU trade, single market, customs union and budget

The white paper reiterates that the government aims to secure “the freest and most frictionless trade possible in goods and services” with the EU outside the single market and via “an ambitious and comprehensive free trade agreement”.

It also wants to be outside the customs union, so it can negotiate its own trade deals, but would like “a new customs agreement”, which should be theoretically possible thanks to new technology. Again, this does not go further than May’s speech.

We are told once more that the UK will not seek to adopt an existing model used by other countries, but try to “take in elements” of the single market in certain areas – in other words, bespoke deals for important business sectors. From the EU perspective, all this is ambitious: it sounds suspiciously like cherry-picking.

The paper plays up the financial services card, which the government plainly considers a strong one: the EU has a clear interest in “mutual cooperation arrangements”, it says, describing the City as Europe’s only global hub for money, trading and investment on which the EU will continue to rely.

It confirms the UK will leave the Euratom treaty, the legal framework for nuclear power, but says a new relationship will be negotiated, and it says the UK’s future status with EU agencies regulating areas such as medicines, aviation, food safety and financial services will also be part of discussions.

And there will be no more “vast contributions” to the EU budget, as May already said.

Trade with other countries; research

The paper repeats May’s pledge to make the UK a “champion of free trade” and says it will seek bilateral free trade agreements and participate in multilateral negotiations through the World Trade Organisation.

It acknowledges Britain “cannot agree new trade deals until after we have left the EU” – a possible bone of contention with the EU27 – but says there is “much we can do to prepare and to achieve now while respecting our obligations as members”.

It also says work is already under way on establishing Britain’s own schedules covering trade in goods and services at the WTO, aimed as far as possible at replicating those it currently has as an EU member.

The paper also says Britain aims to “continue to collaborate with EU partners” on a key part of its new industrial strategy: science, research and technology. Many academics expect this to become considerably more difficult after Brexit.

Security and crime cooperation

As May has already said, the UK will seek to continue working with the EU “to preserve UK and European security and to fight terrorism and uphold justice across Europe”, the paper says.

It says the government will aim to retain and develop existing cooperation in initiatives like Europol, the European arrest warrant, the Schengen information system, the new EU passenger name records, and the European criminal records information system.

In terms of security and defence, it also promises to “remain committed to European security and add value to EU foreign and security policy” – an offer that may well prove valuable in the exit negotiations.

Orderly exit

The white paper says the government aims to deliver “a smooth, mutually beneficial exit” but says this will require “a coherent and coordinated approach on both sides”. Article 50 will be triggered no later than the end of March, it repeats.

It acknowledges it is “in no one’s interests for there to be a cliff-edge for business or a threat to stability”, saying the government would like “to have reached an agreement about our future partnership” by the end of the article 50 process and repeating May’s suggestion of variable “phased processes of implementation” to give everyone time to plan and prepare for the new arrangements.

The paper also reiterates the prime minister’s remarks that “no deal for the UK is better than a bad deal for the UK” – and suggests that, to mitigate against the impact of not getting the deal it wants from the EU, the government will prepare legislation “to ensure our economic and other functions van continue”.

It does not say what the legislation will contain, or what future economic model the government might envisage.