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MP Derek Conway will not be investigated by police.
Scotland Yard has said it would not be "appropriate" to hold an police investigation into the financial activities of the MP for Old Bexley and Sidcup.
Mr Conway was reprimanded by the House of Commons authorities for paying his student son nearly £40,000 for research despite no record of any work being found.
Conway was suspended from Parliament for 10 days and ordered to repay £13,161.
A Metropolitan Police statement said a lack of systems for investigating such matters would simply undermine a criminal investigation.
It said: "The allegations have already been investigated by the Parliamentary Commissioner and then put before the Parliamentary Committee on Standards and Privileges who recommended sanctions that were imposed by the House.
"The CPS advised us that they are of the view that the lack of systems in this case to account for MPs’ expenses would severely undermine the viability of any criminal investigation leading to a prosecution.
"In these circumstances we do not believe that it is appropriate for a police investigation to be instigated."
This statement comes after a chief officer at Scotland Yard wrote to the commissioner in February asking if this matter was going to be investigated.
Mr Conway has said he will stand down as MP for the area at the next general election.