Loredana Sangiuliano/ShutterstockAndy Burnham’s revelation that he was prepared “to go all the way” in terms of the UK’s relationship with the EU came as a shock to many. While a commitment to rejoining the EU in the next Labour manifesto is far from a given – and the prime minister’s language was non-committal – the statement broke a taboo in the party.The idea of “reversing Brexit” seems to be in genuine contention, with Burnham’s advisors assessing public support. Meanwhile, allies in the EU seem to be taking the idea seriously, with the French president, Emmanuel Macron, promising to welcome the UK back.In practical terms, it is not difficult to see why the idea of rejoining is tempting. The UK economy is languishing, in part due to the estimated 6% cost of Brexit to GDP. The UK follows many EU rules in practice anyway, but lacks the unfettered market access that would come as a member.Brexit benefits have been hard to find outside ill-defined ideas of “taking back control” or rebuilding national self-confidence. Meanwhile, much has changed in the UK’s external environment. Russia invaded Ukraine just over a year after the UK ended formal security cooperation with the EU, and the second Trump administration appears to have little love for the US’s traditional Nato allies. Commonwealth countries, especially Canada, Australia and New Zealand, appear to be moving closer to the EU than they are to the UK.The limits of the resetThe idea of rejoining the EU also reflects the limitations of the “reset” begun under Burnham’s predecessor Keir Starmer. Since the Brexit referendum in 2016, the most difficult challenge has been squaring UK and EU “red lines” for continued cooperation. For the EU, these focus on ensuring the integrity of the single market and the balance of rights and obligations. For the UK they have involved an aversion to free movement and to the sovereignty cost of being subject to the rulings of the European Court of Justice.These constraints meant the options available to the UK were highly restrictive. Essentially, it can be either a rule-taker under the “Norway model” (membership of the single market via the European Economic Area), or agree a more limited free trade agreement as the UK eventually did. Bespoke arrangements are not on offer and never will be.This tension confronts pro-Europeans and soft Brexiteers most starkly. The same logic that made life difficult for former PM Theresa May continues to bedevil the reset.Efforts under Starmer to rebuild the relationship have turned out to be more difficult than expected. There has been slow progress on emissions trading and agri-food issues, and a high price tag for the UK’s participation in EU programmes, such as the defence procurement scheme known as Safe.Faced with the prospect of decades of costly, piecemeal re-engagement through the reset or becoming a rule-taker via single-market membership from the outside, Burnham could well decide that the radical option with the greater payoff is more desirable.Politically, putting rejoining the EU on the table is more difficult to understand. Brexit produced a schism that successive governments have been keen not to reopen.It has proved to be a successful mobilisation tool on the right. Conservative PM Boris Johnson forged a broad coalition in December 2019 by claiming Brexit was under threat, and his successors have turned their attention to the European Court of Human Rights now that the EU is out of the picture.Burnham may believe that a clearer position could attract pro-EU constituencies that have moved to the Greens, the Liberal Democrats or the SNP. He may also have calculated that if Labour is going to be accused of betraying Brexit in any case – as Reform UK has claimed – then it makes sense to go the whole way.He may also be banking on the data which show that many UK citizens feel Brexit has gone badly, with a clear majority (57%) believing it to have been a mistake. But dislike of Brexit does not necessarily mean support for rejoining. Many citizens are just tired of the issue by now.The challenges of rejoiningThe process itself may be painful – and could throw up curveballs. The UK would need to negotiate the terms of re-accession and seek to regain its opt-out on joining the euro. It would also need to implement EU rules passed since Brexit, many of which the UK would not have supported in their current form – most notably the AI Act (amid fears it could stifle innovation).The UK would be rejoining from a position of weakness and would be subject to the demands of individual member states. Any of these could veto the decision. And while European leaders seem open to the idea now, enthusiasm for closer ties with the UK has a notable tendency to diminish over time.Fears that the UK could act as a disruptor, or even the risk of a second Brexit, might limit support for the UK rejoining. And political change in France and Germany could bring about governments less favourable to the prospect.It is early days – and Burnham’s words may come to nothing. But the conversation is unlikely to stop here. Through the mere suggestion, the prime minister has rekindled the prospect that one day Britain will return to the EU. Expect more mentions of rejoining in future as the UK yet again grapples with the trade-offs involved with EU membership.Benjamin Martill is affiliated with Chatham House and the Independent Commission on UK-EU Relations and has previously received funding from the European Union’s Horizon 2020 research and innovation programme.