* Late-night votes on central plank of UK Brexit plan

* Government wins, but more serious tests to come

* Labour opposes bill saying it amounts to a power grab

* Pro-EU Conservative rebels saving objections for later (Adds vote result, PM May comments)

By Kylie MacLellan and Elizabeth Piper

LONDON, Sept 12 (Reuters) - Britain's parliament backed a second reading of legislation to sever ties with the European Union early on Tuesday, a reprieve for Prime Minister Theresa May who now faces demands by lawmakers for concessions before it becomes law.

After more than 13 hours of speeches for and against the legislation, which May says is essential for Brexit but critics describe as a Conservative government power grab, lawmakers voted 326 to 290 in favour of moving the EU withdrawal bill, or repeal bill, to the next stage of a lengthy lawmaking process.

Many fell in step with the government which said a vote against the legislation would force Britain into a chaotic exit from the EU, rather than a smooth departure, as the country would lack laws and a regulatory framework to steer the process.

May, weakened by the loss of her majority in a June election, now faces a battle against politicians who want to force amendments to the bill, first in the lower house of parliament and then in Britain's unelected upper chamber.

"Earlier this morning parliament took a historic decision to back the will of the British people and vote for a bill which gives certainty and clarity ahead of our withdrawal from the European Union," May said in a statement.

"Although there is more to do, this decision means we can move on with negotiations with solid foundations and we continue to encourage MPs (lawmakers) from all parts of the UK to work together in support of this vital piece of legislation."

Her justice minister urged lawmakers to back the bill and signalled that the government would listen to the concerns of lawmakers despite describing some of their criticism as being "exaggerated up to and beyond the point of hyperbole".

The bill seeks largely to 'copy and paste' EU law into British legislation to ensure Britain has functioning laws and the same regulatory framework as the bloc at the moment of Brexit, to offer some reassurance for companies.

REFERENDUM RIFT

But the often impassioned debate in the 650-seat parliament underlined the rifts exposed by last year's EU referendum, not only in Britain's main parties, but also in the country.

The opposition Labour Party had called on its lawmakers to vote against the bill if the government failed to make concessions. But seven rebelled, with some saying they had to respect the demands of their pro-Brexit voters.