A weakened Theresa May came under fresh pressure Tuesday to soften her Brexit position, adding to uncertainty about her negotiating strategy with Brussels one year after she became Britain's leader.

The prime minister marked the anniversary with a speech in which she appealed to the main Labour opposition party to help implement her policies, a month after losing her majority in a general election.

Amid rumours of plans to oust her, May accepted that "the reality I now face as prime minister is rather different" than it was before the June 8 election.

May took over last year after her predecessor David Cameron resigned in the wake of a shock referendum in which Britain voted to leave the European Union.

The austere vicar's daughter was seen as a safe pair of hands who could heal a Conservative Party that emerged bitterly divided from the referendum.

But her government has been forced into a series of embarrassing U-turns and her gamble of holding an early election backfired spectacularly.

Key parts of her Brexit plan are now also under fire from critics within her own party who want a more moderate approach and whose voices are suddenly influential because of the election result.

The latest fronts in the battle between proponents of a "hard" and "soft" Brexit are Britain's membership of the Europe's nuclear regulator Euratom and the authority of the European Court of Justice.

Some Conservative MPs have reportedly warned they will rebel if May pushes ahead with her plan to withdraw from Euratom after doctors said it could jeopardise treatment for cancer patients.

The government has also hinted it may relent on its hardline position of ending the authority of the EU's highest court in Britain from the moment the country leaves the bloc as expected in 2019.

- 'Avoid rocking' the boat -

The real showdown is expected after the government on Thursday publishes the Repeal Bill, a hefty draft law aimed at scrapping the cornerstone of Britain's EU membership, the European Communities Act.

The opposition is already planning amendments to the bill, which would also adopt, amend or repeal thousands of EU laws that currently apply in Britain.

Vince Cable, a member of the pro-EU Liberal Democrats, has said the doubts over Britain's withdrawal from the EU mean it may not happen.

"I'm beginning to think that Brexit may never happen," he told the BBC's Andrew Marr Show on Sunday.

"The problems are so enormous, the divisions within the two main parties are so enormous I can see a scenario in which this doesn't happen," he said.

The stormy mood among Conservatives prompted former party leader William Hague on Tuesday to ask: "Is it worth having a huge row to insists on a 'purer' version of Brexit? No of course it isn't."

Writing in the Daily Telegraph, he urged Conservative MPs to "avoid rocking that very vulnerable boat".

May's influence in the House of Commons took another dent on Monday when one of her MPs, Anne Marie Morris, used a racist epithet at a pro-Brexit meeting and was suspended from the parliamentary party.

Rumours have swirled in recent weeks about possible plots against May from within her own cabinet.

One possible alternative put forward is her Brexit minister David Davis, who has dismissed the reports.

Davis is due to address a parliamentary committee later on Tuesday in which he is expected to be pressed to clarify the government's strategy.