The club, founded in 1885 and currently based in Richmond-upon-Thames in south-west London, were relegated from the Premiership in 2015.
Founded by the Welsh community in London, the club provided a string of players to the great Wales and British and Irish Lions teams of the 1970s but fell on hard times in recent years.
"Following the appointment of Liquidators in December 2016, a temporary licence was granted by the RFU to London Welsh to enable participation in the Championship," the English RFU said in a statement.
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The licence expired on Saturday and the club failed to meet the conditions required by the regulations.
"With regret London Welsh will no longer be granted permission to play in the Championship for the remainder of this season and beyond," the RFU added.
The decision means London-based amateur side Richmond, bottom of the standings, are guaranteed another season in the Championship.
(Reporting by Ed Osmond; Editing by Keith Weir)
