LONDON- Britain's opposition Labour Party has done all it can to reach a Brexit compromise with Prime Minister Theresa May but is deeply concerned a future Conservative leader could renege on any promises made by the current government.

Labour's second most powerful man, finance chief John McDonnell, said a customs union was absolutely key for the party and there was not yet a deal.

"We haven't seen the significant shift yet that we require to be able to support a deal," McDonnell said. "We are not near what we want."

When asked by Reuters if the talks were doomed, McDonnell said: "We have gone into them in good faith and we've done everything we possibly can to try to reach a traditional British compromise."

He said a letter from former British ministers including Boris Johnson - who could be the next leader of the Conservative Party - demanding that May refuse to agree a post-Brexit customs union had not helped.

"What we are all concerned about is the letter from Boris Johnson which said one he wouldn't accept a customs union, one of our key elements, and secondly that if he was leader, and he may well be, that he would overturn any deal that we'd agreed."

"That doesn't inspire confidence in the ability to secure a deal that lasts longer than a couple of months," McDonnell said.

McDonnell compared the Brexit negotiations with May's government to trying to make a contract with a company which was about to go into administration.

May, who has offered to quit if parliament accepts her Brexit deal, opened cross-party talks with the Labour Party more than a month ago after parliament rejected her European Union withdrawal deal three times.

The discussions with Labour are a last resort for May, whose party’s deep divisions over Brexit have so far stopped her getting approval for an exit agreement and left the world’s fifth largest economy in prolonged political limbo.

(Reporting by Andrew MacAskill and Guy Faulconbridge) ((; 07825218698;))