Andy Burnham is planning to push for a deal to hand power over Britain to EU judges as part of a new migration pact.
The move would be considered a major blow to the 2016 Brexit vote as Boris Johnson made “taking back control” a cornerstone of the Leave campaign.
The subsequent Brexit deal was proof that sovereignty was being restored to Westminster, dragging power back to British judges.
Previously, Mr Burnham blamed leaving the bloc for the rise in small boat crossings. After weeks of soft-launching his bid to rejoin the EU, Mr Burnham is now eyeing up an agreement with Strasbourg whereby the UK can access databases of asylum seekers and criminals.
But, in exchange, EU officials said that the UK must buckle to oversight from the European Court of Justice (ECJ) – as well as cough up an extra fee to do so, The Telegraph revealed.
Alex Burghart, the Shadow Chancellor of the Duchy of Lancaster, said: “Labour’s EU Reset treats a closer relationship with Brussels as a panacea, while ignoring the very real trade-offs it would bring for farmers, fishermen and taxpayers.
“If access to EU databases means handing over taxpayers’ money and accepting ECJ oversight, Labour must explain the price. You cannot put a price on sovereignty,” he told The Telegraph.
The move comes after Mr Burnham claimed Brexit had made the small-boat crisis worse and suggested he could support rejoining the union.

