The former Prime Minister’s institute issued a report calling for closer ties to Brussels and alignment on some of the rules and regulations it issues.
But government insiders dismissed the plan to “fix Brexit” issued by the Remainer’s office.
A source said: “The Labour Party have made clear their opposition to Brexit so there’s no surprises here.”
“The Prime Minister has been clear that the current Brexit deal – the Trade and a cooperation Agreement – can deliver enormous benefits for our country.”
“As he said in his CBI speech last week, under his leadership the UK will not pursue any relationship with Europe that relies on alignment with EU rules.”
The report from the Tony Blair Institute for Global Change calls for the deal secured by Boris Johnson to be “revisited”.
It says a UK-wide agreement with the EU on food safety regulations should be negotiated in order to fix problems with the Northern Ireland Protocol
Ministers should be allowed to align voluntarily with parts of the EU single market for goods, according to recommendations.
It adds that a business consultation should be launched to inform the UK government’s negotiating approach when the Trade and Cooperation Agreement is up for review in 2025.
Anton Spisak, senior fellow at the institute, said: “Most of the British public recognise that Brexit in its current form isn’t working for anyone.”
“What has now changed for the first time since leaving the EU is that there is political space to discuss not only Brexit’s consequences but what improvements are necessary to the future relationship with the EU.”
“Our report sets out a new policy agenda to fix Brexit’s ongoing practical problems and find a new more balanced relationship with the EU.”
“With the country facing recession and the steepest decline in living standards on record, the current government should take a pragmatic approach to fixing Brexit. This is also critical to providing certainty in Northern Ireland. Failing that, it will be incumbent on the next government to pick up the pieces and deliver tangible solutions to the problems arising from Brexit.”