British MPs on Wednesday backed Prime Minister Theresa May's newly-revised plan for leaving the European Union -- which raises the possibility of delaying Brexit.

Lawmakers approved a three-step plan unveiled by the embattled leader on Tuesday that would give her more time to renegotiate an agreement struck with the bloc last year.

If she fails to win MPs' support for her reworked deal by March 12, they will then vote on March 13 and 14 on leaving the EU as scheduled on March 29 without an agreement -- or delaying Brexit.

Lawmakers showed overwhelming support for the proposal, approving by 520 votes to 20 an amendment tabled by Labour former minister Yvette Cooper seeking to bind May to the timeframe. 

MPs also voted on several other amendments from backbenchers, including approving without a vote Conservative Alberto Costa's stipulation that May must seek a treaty on citizens' rights after Brexit under any scenario.

Costa quit his junior government post, an unpaid role as parliamentary private secretary in the Scotland Office, earlier Wednesday in order to bring the amendment -- which the government then backed.

Meanwhile an amendment put forward by Labour main opposition leader Jeremy Corbyn, calling on the government to adopt Labour's preferred Brexit position, was comfortably defeated.

The motion, instructing the government to negotiate a permanent customs union with the EU and close alignment to the single market, was beaten by 323 votes to 240.

Corbyn announced Monday that Labour would support a second Brexit referendum if the amendment was defeated.

A motion from the Scottish nationalists requiring Prime Minister Theresa May to rule out immediately a no-deal Brexit "under any and all circumstances" and regardless of exit date was beaten by 324 votes to 288.