Mr Burnham did say the 'last thing' the Government should do was 're-run' the EU membership arguments

Britain could be hit with a £35billion bill if Andy Burnham rejoins the European Union (EU), according to pro-Brexit researchers.

The estimate from the campaign group Britain Unbound is based on Brussels’ proposed budget plans for 2028 through to 2034.

EU officials are planning to raise member spending to nearly €2trillion over a seven-year period and introduce new taxes on carbon emissions, tobacco sales and electronic waste.

Britain Unbound boss Steve Wright told The Sun: "Those who wish to rejoin the EU should present their argument in the harsh reality of the present day. Not a rose-tinted picture of 2016."

The figure is based on a hypothetical scenario where the UK joins the EU in 2028 ­without negotiating a rebate or opt-outs.

Shadow Foreign Secretary Dame Priti Patel said rejoining the bloc would lead to "yet more tax rises".

Last September, Mr Burnham said he wanted the UK to rejoin the EU "in my lifetime", but quickly rowed back on his comments.

He said: "My view is that Brexit has been damaging, but I also believe the last thing we should do right now is re-run those arguments.

"I respect the decision that was made at the referendum and it is going to undermine everything I have said about strengthening democracy if we don't respect that vote."

Chancellor Rachel Reeves said earlier this week there was no alliance more important to the UK "than our relationship with the European Union".

Speaking to City leaders at the annual Mansion House dinner, she argued Britain should take a different approach with the bloc, with the UK being "included not excluded" from EU arrangements as standard.

She reiterated her criticism of Brexit, saying: "I have always been clear about the damage that Brexit did to our economy."

"Britain’s future is inescapably bound with that of Europe, our largest trading partner, with whom we share common interests and common values."

However, it is unlikely Ms Reeves will stay in No11 as Mr Burnham succeeds as Prime Minister.

Home Secretary Shabana Mahmood is understood to be the front-runner for the role of Chancellor.

It was previously rumoured Energy Secretary Ed Miliband would be offered the role by Mr Burnham, however, allies of the incoming Prime Minister appear to have succeeded in blocking the job offer.

They told Mr Burnham the Energy Secretary is "divisive", carrying a lot of "baggage" after his unsuccessful bid for No10 in 2015.

He would not pass the "sniff test" with the markets, they argued.

Since Ms Mahmood's name has been mentioned as the likely Chancellor-to-be, the pound has risen to a two-month high against the dollar.

Sterling rose from $1.33 against the dollar in early-morning trading, growing to $1.35 by late-afternoon yesterday.

Sitting on Labour's conservative right, Ms Mahmood is understood to be an EU sceptic, Politico reports.

However, she has voted generally towards greater EU integration (84 per cent), data from TheyWorkForYou shows.

Despite Mr Burnham wanting to continue forming closer ties with the EU, it is understood he is looking to establish a "broad church" Cabinet.