LONDON (Reuters) - British Prime Minister Boris Johnson proposed on Tuesday that lawmakers be banned from acting as paid political consultants or lobbyists, after a row over second jobs posing conflicts of interest.

       Johnson said the code of conduct for members of parliament (MPs) should be updated and those who are prioritising their outside interests over their constituents "should be investigated and appropriately punished".

       The British leader has come under pressure from damaging media reports about lawmakers being paid for external work after his Conservative government sought to change parliamentary conflict-of-interest rules to protect a colleague threatened with suspension.

       Johnson's handling of the affair has been criticised by some in his own party as well as opponents, and recent polls suggested it was having an impact on his standing, with surveys suggesting the opposition Labour Party was now ahead.

       In a letter to the speaker of the House of Commons, he backed measures recommended by parliament's Committee on Standards in Public Life which would ban MPs from accepting paid work as a parliamentary strategist, adviser or consultant, and all second jobs should be within "reasonable limits".

       "They would also ban MPs from exploiting their positions by acting as paid political consultants or lobbyists," Johnson wrote.

       (Reporting by Kylie MacLellan, editing by Estelle Shirbon)