The Commons has amended the EU withdrawal bill to ensure that it will get a vote on any final deal with the EU. So has parliament “taken back control”? Far from it – for two reasons.

First, any such vote will be on the UK’s withdrawal agreement. By the time it comes, perhaps at the end of 2018, it will be difficult, maybe impossible, to make more than cosmetic changes. There will be no appetite in Brussels or among the EU27 member states to renegotiate. And if parliament did reject it, the impact would not be to stop Brexit, but rather to ensure that Britain crashes out of the EU without a deal. Remember, as a result of parliament’s own decision to authorise the government to send the official article 50 notification, we automatically leave the EU on 29 March, 2019, with or without a deal.

Moreover, there is a more fundamental problem. The withdrawal agreement will cover the topics of phase 1 of the negotiation – the deal that was agreed in principle, at a political level, last week. That is, it will cover citizens’ rights, the financial settlement and the Irish border issue. It will also address the “transition” period we are about to negotiate.

Why would parliament want to reject an agreement on any of these? On money, parliament won’t vote to pay more than we agree, and the EU27 certainly won’t accept less. On citizens’ rights, most MPs are happy with the basic principle that EU citizens should be allowed to stay, and don’t understand the technicalities. Voting down an agreement, adequate or otherwise, will do nothing to keep the Irish border open. And while some Brexiteers are understandably unhappy with a so-called “transition” – why would they not be, as it means merely all the rules and obligations of EU membership, but without a voice or a vote – nobody really has a better alternative.

What parliament really wants – and quite right too – is a say about the much more fundamental question that will be discussed in phase 3 of the negotiations – what will the UK’s post-Brexit relationship with the EU look like? Will we seek to maintain, as far as possible, the current degree of economic integration with the EU, even after we leave its political structures? That is, do we seek to remain, formally or through some alternative arrangements, in the EU single market and/or customs union? Or do we seek to disengage and negotiate a “deep and comprehensive trade arrangement” with the EU – that is, a comprehensive free trade agreement, with nothing like the degree of regulatory convergence implied by the single market. The latter would mean a very significant increase in barriers to trade – formal and informal – with our largest trading partner, but on the other hand offers the opportunity to shape our own regulatory framework and to conclude trade deals with the rest of world.

That is a genuinely meaningful choice. It is not one that was on the referendum ballot, and there are former remainers and leavers on both sides of the divide. It is not one that has ever been properly debated or decided, either in parliament or the country. Much of the debate has been of the “cake and eat it” kind. Indeed, Theresa May has so far refused to even have a proper discussion in cabinet, since she knows there is deep disagreement.

On this, the most fundamental issue, the EU27 aren’t seeking to impose their views. As EU representatives have said repeatedly, we have a binary choice to make, but it is our choice. Indeed, at the European council this week, heads of government will say that negotiations can now move to the next phase; but they will also say that discussions on the “framework for the future relationship” can only begin after the UK makes clear what it actually wants. The ball is in our court.

But this is not something that parliament will be able to vote on in when it gets its “meaningful vote” on the withdrawal agreement. By then it will be too late. The UK’s negotiating position on this all-important aspect of Brexit will have to be set out in the next couple of months. If parliament actually wants a meaningful voice on this – perhaps the most important single choice about the future of the UK economy since the mid-1970s – it needs to act now.

It should insist that, before we table anything in Brussels for the phase 2 negotiations, there should be a proper debate in parliament. Let’s settle the things we didn’t and couldn’t decide in the referendum. Do we care more about the freedom to set our own regulations or about being part of the largest single market in the world? Do we care more about ending free movement or about preserving free trade with Europe? Do we care more about “frictionless” borders in Ireland and Dover or about trade deals with the US? These are vitally important political and economic questions, with no “right” answers. And they shouldn’t be left to a weak prime minister and her divided cabinet and party. Now is the time to take back control.

• Jonathan Portes is senior fellow of UK in a Changing Europe