(Recasts with three peers suspended from their parties)

By Estelle Shirbon

LONDON, June 2 (Reuters) - Three members of Britain's upper house of parliament were suspended from their parties on Sunday after media sting operations caught them apparently offering to use their influence for personal gain.

The undercover investigations have thrust the issue of lobbying into the limelight and had already forced a member of the lower house of parliament, Patrick Mercer, to resign from the ruling Conservative Party and seek legal advice.

The three House of Lords peers caught out by a Sunday Times sting operation are John Cunningham and Brian Mackenzie of the main opposition Labour Party and John Laird of the Ulster Unionist Party.

All three denied breaking the chamber's rules but their parties took swift action against them.

"Lord Cunningham and Lord Mackenzie of Framwellgate have been suspended from the Labour Party pending further investigation," the party said in a statement.

Mike Nesbitt, leader of the Ulster Unionists, said in a statement he had called Laird after reviewing the media coverage and as a result of that call Laird had resigned from the party pending an investigation.

The trio were covertly filmed offering to ask parliamentary questions, lobby ministers and host events in prestigious House of Lords premises in exchange for payment by what they were told were lobbyists acting for companies.

The scandal will renew pressure on Prime Minister David Cameron to introduce a statutory register of lobbyists, as promised in 2010 in the coalition agreement between his Conservatives and their junior partners, the Liberal Democrats.

Cameron warned more than three years ago that lobbying was "the next big scandal waiting to happen" but critics, including some Liberal Democrats, accuse him of dragging his feet.

SUSPICION

Sunday Times reporters approached Cunningham, a former minister under then Prime Minister Tony Blair in the 1990s, pretending to represent a South Korean solar energy company.

"Are you suggesting 10,000 pounds a month? Make that ... 12,000 pounds a month. I think we could do a deal on that," he was quoted as saying by the newspaper during a discussion about his fees for what was described as consultancy work.

Cunningham later sent a statement to the Sunday Times saying he had referred to "a fanciful 12,000 pounds a month" to test his suspicion that he was talking to undercover journalists.

"I deny any agreement to operate in breach of the House of Lords code of conduct and, in fact, recall that I made it clear that I would only operate within the rules," Cunningham said.

Laird also issued a statement denying he had broken the rules and Mackenzie denied wrongdoing in two BBC interviews. The three peers could not immediately be reached by Reuters.

Mercer was caught out by undercover reporters from the Daily Telegraph newspaper and the BBC's investigative Panorama programme posing as lobbyists for businesses seeking to end Fiji's suspension from the Commonwealth on human rights grounds.

His resignation from the Conservative Party was no great loss to Cameron as the House of Commons MP was an outspoken critic of the prime minister, but the allegations against him reflect badly on the party and on parliament in general.

Mercer tabled five questions to government and a parliamentary motion on the Fiji issue after being paid 4,000 pounds ($6,100) as part of a bogus contract he believed would earn him 24,000 pounds a year, the two media reported.

He told the fake lobbyists he had persuaded 18 other members of parliament to join an all-party group on Fiji, commenting that they included "several freeloaders that would like to go to Fiji" and one who asked to take his wife, the media said.

($1 = 0.6596 British pounds) (Editing by Pravin Char)