Brexit has depressed UK exports to the EU by 12%, and rejoining the customs union would undo only a fraction of the damage, research shared with the Guardian shows.

With the UK’s future relationship with the bloc likely to feature prominently in a potential Labour leadership contest, the economists John Springford and Anton Spisak, of the Centre for European Reform, provide fresh evidence of the damage caused by exiting.

A decade on from the referendum, they have found that services sector exports to the EU are 7% lower than they would have been if the UK had remained in the EU, and goods exports are 16% lower.

Using detailed trade data and economic modelling, they show that the “overwhelming majority” of the impact – 10% of the total 12% decline in exports – is accounted for by leaving the single market.

“The regulatory costs related to Brexit – such as new certification procedures and checks for compliance with EU standards – have had a much more significant impact on UK-EU trade than customs-related barriers,” they say.

The hardest-hit sectors have been travel, finance and insurance, chemicals and pharmaceuticals, and agrifood.

The estimate of lost services exports is larger than previous research has suggested, because the authors take into account a significant uptick in services trade within the EU since the Covid pandemic that the UK has missed out on.

Keir Starmer and Rachel Reeves have increasingly stressed the importance of striking a closer trading relationship with the EU, with a summit to be held next month.

But the government has said it will stick to Labour’s manifesto promises not to rejoin the single market or customs union, or accept the free movement of people.

More recently, potential leadership candidates Andy Burnham and Wes Streeting have both suggested they would like to see the UK rejoin the EU at some point in the future.

The Liberal Democrats had previously advocated rejoining the customs union as the first step to reversing Brexit, but their leader, Ed Davey, announced this week that the party would now campaign for the UK to re-enter the single market.

The CER research suggests the upside of rejoining the customs union alone would be modest. It would eliminate the need for UK firms to comply with complex “rules of origin”, about where the content of exports comes from, to qualify for tariff-free trade.

But a customs union would have no benefit for the hard-hit services sector, and by analysing which goods exports currently do not comply with the rules, Springford and Spisak suggest the impact on overall trade would be small.

Meanwhile the UK would lose the opportunity to pursue trade deals with non-EU countries, because members of the customs union have to apply EU tariffs.

However, Springford and Spisak point out that the more radical step of rejoining the single market would entail risky political trade-offs, including signing up to the free movement of people, paying into the EU budget and following European rules the UK has had no say in setting.

“The overwhelming majority of the estimated trade impacts stem from leaving the single market. Recovering those losses would entail re-integrating with the EU economy via a single market, either in goods or in full, through a bespoke arrangement or eventual EU membership,” they argue.

“Either path involves difficult political choices: accepting free movement, making budget contributions, and aligning with EU rules without a vote on them. The more privileged the single market access sought by the UK, the greater the obligations it would be expected to accept.”

Reeves has suggested “dynamic alignment” in some sectors, with the UK agreeing to follow EU rules in exchange for increased market access. But Brussels-watchers are sceptical how much further along this route the EU would be willing to go without insisting the UK accept free movement and budget contributions.

Advocates of Brexit argued before the 2016 referendum that increased trade with non-EU countries, as the UK disentangled itself from the constraints imposed by Brussels, would offset any hit to EU trade. But Springford and Spisak find little evidence that this has happened thus far.

They say their findings are consistent with several studies suggesting that Brexit has knocked between 4% and 8% off UK GDP.