Property agent Barnard Marcus said the flat, which is part of Siddons Court, an ex-council mansion block on Tavistock Street, has been snapped up for £1.21m after just six weeks on the market.
It is thought to have smashed the previous record set by a council flat on Fulham Road above the Stella McCartney store, which came on to the market at £1.15m in July.
The Covent Garden home, which is close to the Piazza and Royal Opera House, was bought off the council in 1990 under the Right to Buy scheme for £130,000.
The sale comes at a time of acute affordable housing shortages in London and soaring rents.
According to CBRE the average value of properties sold in the West End in the second quarter was £1.86m, which is 31 per cent higher than the previous quarter and 22 per cent of the same time last year.