On Tuesday morning Sir Malcolm stepped down as chairman of Parliament’s intelligence and security committee and said he would not stand for re-election in May.
He denies any wrongdoing in relation to the comments he made to undercover reporters from the Telegraph and Channel Four’s Dispatches documentary.
They had posed as staff of a fake Chinese firm to film him and fellow former Foreign Secretary Jack Straw.
Sir Malcolm reportedly said he could secure access to British ambassadors around the world.
He referred himself to Parliament’s standards watchdog on Monday following the revelations about the secret filming.
In a statement on Tuesday morning he said: “None of the current controversy with which I am associated is relevant to my work as chairman of the intelligence and security committee of Parliament.
"However, I have today informed my colleagues that while I will remain a member of the committee, I will step down from the chairmanship.
“The committee is due to be dissolved in little over a month with the prorogation of Parliament for the forthcoming general election.
"I do not want the work of the committee and the publication of the report to be, in any way, distracted or affected by controversy as to my personal position. I have concluded, therefore, that it is better that this important work should be presided over by a new chairman."
He said the allegations made against him by the Telegraph and Channel 4 were "contemptible". He had intended to retire as an MP in 2020, but would not stand this year in order to remove "uncertainty" during the election campaign.
In interviews on Monday, Sir Malcolm said his usual fee for half a day’s work was between “£5,000 and £8,000”.
The UJIA £5,000 fee was for a keynote speech at the Savoy hotel in central London. The event raised around £200,000.
A UJIA spokeswoman said: “Like all charities, we endeavour to secure the very best guest speakers who will also support our events for free. It is not always possible to achieve this, therefore, sometimes we have to pay a fee for a speaker.”
