LONDON, Nov 17 (Reuters) - British lawmakers on Wednesday backed moves to curb their ability to take second jobs in addition to their work in parliament, although opposition parties said Boris Johnson"s Conservative government had watered down the proposals. Prime Minister Johnson has come under pressure to act after two weeks of damaging headlines about members of parliament (MPs) being paid for external work, with some earning large sums and others possibly in breach of standards rules. The "sleaze" scandal erupted earlier this month after Conservative lawmakers, acting with Johnson"s support, voted to halt a proposed 30-day suspension of Owen Paterson, a former minister, who had been found guilty by parliament"s standards watchdog of repeatedly lobbying for two firms. read more On Wednesday, parliament rejected an opposition Labour Party motion to support proposals to ban lawmakers from carrying out any paid work as a parliamentary adviser or consultant. Instead, a government amendment was passed which called for cross-party talks and for parliament"s Committee on Standards to bring forward recommendations for new rules for MPs by the end of January. "This means that MPs will be banned from acting as paid political consultants or lobbyists and that MPs are always prioritising their constituents," a government spokesperson said. Labour said the government amendment was vague and non-binding. "We are not going to back down from these proposals," Labour leader Keir Starmer told Sky News. "We"re not prepared to have them watered down." Johnson"s handling of the sleaze row has been criticised by some in his own party as well as opponents, and some opinion polls show a fall in support for the Conservatives. The prime minister only finally acknowledged at a parliamentary committee hearing on Wednesday that Paterson had broken lobbying rules. Johnson was given a cool reception by Conservative lawmakers at a private meeting in his Downing Street office ahead of the vote, according to one MP who was present. Johnson repeatedly apologised for his handling of the affair, the lawmaker, speaking on condition on anonymity, told Reuters.