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MP Derek Conway will not be investigated by police.
Scotland Yard said it would not be “appropriate” to hold a 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 almost £40,000 for research, despite no work being found.
The backbencher 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 been investigated by the Parliamentary Commissioner and put before the parliamentary committee on public standards and privileges, who recommended sanctions that were imposed by the House.
“The CPS advised the lack of systems to account for MPs’ expenses would undermine the viability of a criminal investigation leading to a prosecution.
A police investigation is not appropriate. ”
Mr Conway has said he will stand down as MP for the area at the next general election.