LONDON (REUTERS) - The British government does not yet have the support of enough lawmakers to win a parliamentary vote on its Brexit deal but a "significant number" of colleagues are coming around to back the plan, finance minister Philip Hammond said on Sunday.

Prime Minister Theresa May is expected to bring her deal back to parliament for a third vote this week, but Hammond said it would only go ahead if the government thought it could win.

"What has happened since last Tuesday is that a significant number of colleagues, including some very prominent ones who have gone public, have changed their view on this and decided that the alternatives are so unpalatable to them that they on reflection think the prime minister's deal is the best way to deliver Brexit," he told BBC's Andrew Marr programme.

Asked if the government had enough numbers yet, he replied: "Not yet, it is a work in progress."

British lawmakers rejected May's deal by 149 votes on March 12.

Separately, Opposition Labour leader Jeremy Corbyn has written to lawmakers from across Britain's parliament to discuss ways to break the Brexit impasse.

In a letter written to lawmakers from all parties in parliament, Corbyn invited them to meet with him and his Brexit policy chief Keir Starmer to discuss how to "break the Brexit impasse", and use as a starting point Labour's alternative plan and its support for a vote to prevent a "damaging Brexit".

"It must now be incumbent on us all as parliamentarians to do our best to work together and find a compromise and a solution that ends the needless uncertainty and worry that the government's failed Brexit negotiations have caused," Corbyn said in his letter.