LONDON (REUTERS) - National parliaments should have a greater role in European Union decision making, a committee of British lawmakers said on Monday, including working together to propose new legislation or changes to existing European law.

Under pressure from eurosceptics in his Conservative party as well as the UK Independence Party, British Prime Minister David Cameron has promised to reshape Britain's ties with the EU, then to give Britons a vote on whether to leave the 28-nation bloc, if he wins a national election next year.

National parliaments being able to work together to block unwanted European legislation was among areas of planned reform he set out earlier this month.

Monday's report by the House of Lords EU Committee -a group is drawn from Britain's upper house that aims to influence the government's position on Europe and hold it to account for its actions - proposes a 'green card' procedure to enable national parliaments to work closer together to propose laws.

The EU currently has a "yellow card" system which gives national parliaments an opportunity to object to legislative proposals. If at least a third of EU national parliaments submit such objections, a "yellow card" is triggered and the EU has to review its proposal.

"There should be a way for a group of like-minded national parliaments to make constructive suggestions for EU policy initiatives which may include reviewing existing legislation, complementing the existing 'yellow card' with a 'green card'," the report said.

The committee of lawmakers also suggested the "yellow card" system should be strengthened, including extending the deadline for raising concerns to 12 or 16 weeks from eight weeks, and requiring the EU to withdraw or substantially amend any legislation which is objected to.

"National parliaments have a vital role to play in ensuring EU institutions are accountable to the public they serve," said Timothy Boswell, chairman of the committee.

"That role can be developed without treaty change and the first step is for national parliaments to get better at working together and engaging actively with the European Commission early in the legislative process."

The committee also said that probable closer euro zone integration and central EU control over domestic economic policy following the European financial crisis made it vital national parliaments are given more control over future developments.