LIZ Truss could hardly have had a worse first month as Prime Minister. Creating huge instability in financial markets and concomitant damage to the economy has given Labour a huge lead in the polls, albeit not in Scotland. Yet, curiously, amidst this political mayhem, Liz Truss has taken a few steps to improve UK-EU relations.

Around 60 per cent of UK voters now think Brexit was a mistake. But both Labour and the Conservatives agree that there should be no question of the UK rejoining the EU. Sir Keir Starmer insists he will make Brexit work while emphasising that Labour would not, in government, rejoin the EU single market or its customs union.

This certainly sets up clear blue water between the two main pro-Union parties and the Scottish National Party's aim of independence in the EU. And yet, it also raises the question of whether better EU-UK relations, especially under a likely Labour government in two years’ time, might ease some of the challenges of an independent Scotland being an EU member state while the rest of the UK stays outside.

The few positive moves from Liz Truss are small but notable. She attended the inaugural meeting of the European Political Community in Prague last week – an intergovernmental, pan-European grouping, bringing together 44 countries, the brainchild of France's President Macron. Ms Truss and Mr Macron met on the sidelines of the meeting, friends not foes, jointly announcing a renewed bilateral agenda, including a UK-France summit in 2023.

Meanwhile, the UK is now re-building its links with the so-called North Seas Energy Cooperation grouping, which it had left after Brexit. Most importantly, but unpredictably, Liz Truss has overseen a substantial shift in the mood music around the Northern Ireland Protocol. New political and technical talks are under way. Whether this will finally resolve the stand-off over the Protocol, is the big unknown.

For Labour, Sir Keir’s EU strategy is a balancing act of continuing with Brexit while working to build positive relations with Brussels. Showing his calm, co-operative approach would solve the Protocol problems has been one key part of his strategy. But if Ms Truss does do a deal with the EU on the Protocol, rather than creating a new row, that’s one less contrast for Labour’s EU policies.

Still, there is more. Sir Keir aims to do a veterinary deal with the EU, signing up to EU agri-food health and safety standards, which could ease UK-EU trade all round. Likewise, a Labour emphasis on mutual recognition of qualifications to ease barriers to trade in services, and alignment on EU regulations in sectors such as cars and chemicals, could make hard Brexit trade barriers that bit softer. That all crucially depends on EU agreement. Cherry-picking the EU single market is not on the cards. But there is, unsurprisingly, much more warmth in Brussels for a future Labour government than for any of the post-Brexit Tory ones.

Where does this leave the SNP’s arguments for independence in the EU? Nicola Sturgeon emphasised, in her conference speech on Monday, that Labour supports a hard Brexit just like the Tories. That’s hard for Labour to rebut given Sir Keir’s refusal to rejoin the EU single market and customs union, despite his aim to ease trade barriers. And so, the SNP will continue to underline that the only route back to the EU is via independence.

But the thorny question of the impact of an EU border lying between an independent Scotland and the rest of the UK remains. The irony is that question might get somewhat less tricky if a Labour government does dismantle some of the barriers to trade.

Sir Keir’s push to ease barriers to EU-UK services trade could be particularly helpful. The majority of Scotland’s trade with the EU is in goods, but with the rest of the UK it’s in services. Easier EU-UK trade under Labour, is easier England-Scotland trade under independence in the EU, though only up to a point.

Border issues will also be helped, if Scotland becomes part of the UK-Ireland Common Travel Area, with the double benefit of free movement across the UK and across the EU.

EU candidate countries are also meant to show that, as far as possible, they have good relations with neighbouring countries. It would be important to show that Scotland-England relations are not particularly fractious. An agreed divorce would need to be a friendly one.

But if the UK has better bilateral relations with the EU, co-operating on big energy and security challenges, this will tend to make things easier for an independent Scotland. It would be able to join the bi-annual European Political Community summits immediately on independence, a friendly partner to the UK and the other 43 participating states. And it wouldn’t be joining an EU at loggerheads with the UK.

There might, though, be a rather more political risk for the pro-independence side. A better EU-UK relationship could make EU member states less sympathetic to Scotland’s independence ambitions. Back in 2014, the EU was notionally neutral but clearly rather supportive to fellow member state the UK. And, after six years of different Conservative prime ministers creating extremely difficult EU-UK relations, Brussels will not want to upset a more constructive, less histrionic association with London.

But the UK will remain a third country outsider. And if Scotland chooses independence in the EU, it’s hard to see the EU adopting its 2014 language of suggesting Scotland’s EU accession path would be long and difficult. Even so, some EU governments will look with concern at a fracturing UK and the potential for renewed instability.

But, overall, if the UK and EU start to get on better, with more co-operation on security, migration and trade – even under a Tory government and more so under a Labour one – that is positive in itself. And, both politically and economically, an independent Scotland would benefit from that smoother relationship – first as a candidate for EU membership and, ultimately, as an EU member state.

Read more by Kirsty Hughes:

Why Truss will have to think hard before reneging on the EU

The bonfire of EU laws has the UK Union on the ropes