(Changes date, adds Labour, Conservative comment, context)
By David Milliken and William James
LONDON, May 5 (Reuters) - British Prime Minister Theresa May on Sunday stepped up calls for Labour Party leader Jeremy Corbyn to agree a cross-party deal to leave the European Union, following poor results for both parties in local elections on Thursday.
The parties have been in negotiations for over a month to try to broker a Brexit deal that can secure majority support in parliament, after May's minority government suffered three heavy defeats on her preferred deal this year and was forced to delay Britain's departure.
"To the leader of the opposition I say this: Let's listen to what the voters said in the local elections and put our differences aside for a moment. Let's do a deal," she wrote in the Mail on Sunday newspaper.
Labour responded by saying any deal should be done quickly, but accused May of leaking details of the compromise under discussion and jeopardising the talks.
May's Conservatives lost more than a thousand seats on English local councils that were up for re-election, and Labour - which would typically aim to gain hundreds of seats in a mid-term vote - lost 81.
The talks 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.
The Sunday Times reported that the Conservatives would offer new concessions to Labour when talks restart on Tuesday, including a temporary customs union with the EU until a national election due in June 2022.
"At that point Labour could use their manifesto to argue for a softer Brexit if they wanted to and a new Conservative prime minister could argue for a harder Brexit," a source cited by the Sunday Times said.
Labour's Corbyn has made a permanent customs union with the EU a condition for supporting May's Brexit plans, while most Conservatives oppose a customs union as it would stop Britain from reaching its own trade deals with other countries.
JEOPARDISED
The report on the terms of a possible compromise angered Corbyn's senior ally John McDonnell, who oversees the party's finance policy and has been involved in the Brexit talks.
Asked if he trusted May, McDonnell said: "No, sorry. Not after this weekend when she's blown the confidentiality... I actually think she's jeopardised the negotiations for her own personal protection."
Nevertheless, McDonnell said talks would continue this week and if a deal could still be struck, it must be concluded quickly.