(Updates to reflect that debate has ended)

LONDON, Feb 6 (Reuters) - British lawmakers on Monday rejected the first set of proposed amendments to legislation that would give Prime Minister Theresa May the right to notify the European Union of Britain's intention to leave the bloc.

During seven hours of debate, lawmakers voted against a series of attempts by pro-EU lawmakers to attach extra conditions to May's plan to begin divorce talks by March 31.

Monday's votes were on the issues of parliamentary scrutiny of the withdrawal process and the involvement of Britain's devolved administrations.

Further votes, on which the government could face greater opposition, are due to take place on Tuesday and Wednesday.

Earlier on Monday, May warned lawmakers not to obstruct the will of the British people with amendments to her Brexit legislation, saying she wanted to get on with divorce talks with the EU.

"Our European partners now want to get on with the negotiations, so do I, and so does this house," May told parliament before the debate began.

"The message is clear to all, this house has spoken and now is not the time to obstruct the democratically expressed wishes of the British people. It is time to get on with leaving the European Union."

May has said she expects to win approval from lawmakers in time to stick to her end of the March deadline for triggering Britain's exit from the EU.

On Tuesday lawmakers will continue their scrutiny of the legislation, debating amendments on the final terms of Britain's withdrawal from the EU as well as those calling for the publication of assessments on the impact of Brexit.

The bill is expected to complete its passage through the lower House of Commons on Wednesday. It will then be passed to the upper House of Lords.

(Reporting by Kylie MacLellan, Elizabeth Piper and William James; Editing by Matthew Lewis)