Finally, we have something Brexit-related to agree on: most of us, regardless of how we voted in the referendum, think negotiations with the EU are going badly. According to a poll published on Friday, only 1% think talks are proceeding “very well” and 11% say things are going “quite well”. None of which is good news for anyone who lives in the UK and has to live with the catastrophic consequences of botched negotiations. But the sorry state of these vital talks has given the Labour party scope to vaunt some EU-related credentials, as Jeremy Corbyn met Michel Barnier and three European prime ministers in Brussels last week. The party is routinely blasted by British commentators of all stripes for being too weak, too vague, or too Brexity on Brexit – which makes the positive reception it gets in mainland Europe all the more striking in contrast.

This cordial welcome on the continent can be explained by variations on one theme: credibility. Now seen as a government-in-waiting and a powerful influence in parliament, Labour’s Brexit position matters more to EU negotiators, and has led to several meetings: Corbyn and others have met EU officials at least once since the snap election in June. Last week’s warm exchanges were inevitably compared to the forlorn images of prime minster Theresa May in the Belgian capital for Brexit negotiations. EU officials are apparently keen to talk to the Labour leadership because they are seen as the adults in the room – especially when set against the squabbling Tories. EU reps are getting mixed messages; they don’t know if May’s Brexit talk is real or purely intended to placate her party, so they are looking to Labour for a sense of where Britain stands on key issues.

The party focus on friendly engagement highlights a key distinction in negotiating approach: Labour ministers and MEPs put a premium on building trust and good faith, however divergent are the aims of the two sides at the table – because that’s how good deals are agreed. In contrast, the Tories have an air of wanting to win one over Europe, their negotiating strategy seems more like trying to beat down a dodgy used-car dealer. In this context, Labour’s pledge to guarantee the rights of EU nationals in the UK isn’t only a matter of principle: it establishes trust with the EU negotiating partners representing those citizens. One Labour MEP told me that they are currently working to smooth over upset and offence caused by Conservative ministers: “Rebuilding bridges that the government is pulling down.” This engagement counts when it comes to forging trade and other relations with Europe after Brexit.

Also significant is that Labour is now a source of inspiration for European parties keen to know how their UK counterpart bucked the polling slump blighting centre-left parties from France to Germany, the Netherlands and Spain. That much was evident in the ovations for Corbyn’s speech to the Party of European Socialists in Brussels last week, as he urged sister parties to ditch austerity and neoliberalism and offer a radical left alternative. These solid ties and relationships might matter when it comes to the ratifying of any EU withdrawal agreement, as these European parties, such as the French socialist party or the German SDP, function within those European parliaments charged with doing so. So on the one hand, we have Labour last week telling its European sister parties that they together can beat the far right; while on the other we have a Conservative party that cut ties to the European centre-right affiliation in 2009 under the leadership of David Cameron.

Remainers may be less than thrilled at the idea of Labour stepping in to save Brexit, perhaps preferring a scenario where the Conservatives mess it up completely. Opinions vary according to what you think it is possible to achieve in the time left before the UK’s exit deadline of March 2019. Some think Labour has a duty to stop Brexit no matter what, and to hell with the small detail that a Britain organised around democratic principles did in fact vote to leave. Others counter that, barring a significant shift in public opinion, the opposition’s responsibility is to ensure Brexit is the best (or least bad) it can be. We can feed into this camp the latest numbers crunched by former YouGov president Peter Kellner, who notes that voters are now turning against Brexit, but not in sufficient numbers or constancy – yet – for Labour to shift its policy.

For now, the party is setting crucial terms with its straight “no way” to a no deal and insistence on a transitional period. But it will need to set out more of its stall as negotiations proceed to post-Brexit trade agreements with the EU, to maintain scrutiny of the government’s position. It’s also at this point that you’d expect more engagement with the economic forecasts surrounding Brexit, including the government’s own assessments which it has refused to release. Of course, Labour’s EU dealings will be portrayed negatively by a hyperventilating rightwing media that casts anything shy of full-throated EU-loathing as evidence of treason. Yet the snap election result showed little appetite for this to be the guiding sentiment of talks with the EU. Such fuelling of hatred and animosity might win a Brexit vote. But political grownups know that it can’t win a decent Brexit deal.

• Rachel Shabi is a writer and regular broadcast news commentator