Ahead of the auction house's 'The Grand Marques of the World' sale on Thursday, the car was unveiled in Paris prior to its sale on July 5.
Motorsport.com understands that this particular FW14B took Mansell to five out of the nine victories he scored that season.
Due to its complex period electronics that included traction control and active suspension, the FW14B remained dormant until Williams' 40th anniversary celebration at Silverstone in 2017.
It was then driven by ex-F1 driver Karun Chandhok, who is the official driver of the Williams Heritage division.
This is not the first time a grand prix with such provenance has been sold by Bonhams.
Bonhams motorsport director Mark Osborne told Motorsport.com: "This is really as good as it gets. This car contributed more towards the championship in 1992 over any other car.
"The fact that it was a great Adrian Newey design, and he is still so utterly relevant today as he was then, means I would say it's one of the most important grand prix [cars] ever to come onto the market."
At its Monaco sale last year, chassis six of the 1993 McLaren MP4/8s – the car which Ayrton Senna drove to his sixth and finale victory in the principality – and the Toleman-Hart TG184-2 which Senna drove in the famous rain-soaked 1984 race to finish second to Alain Prost were also sold.
Reportedly, former F1 boss Bernie Ecclestone won the bidding on the MP4/8 at €4.1million, equivalent to £3.6m at the time.
That meant it fell well short of the £5.7m record auction fee ever paid for an F1 car, when Michael Schumacher's F2001 Ferrari was sold by Sotheby's in New York in November 2017.
A group photo next to the Williams FW14B Renault
Sam Bloxham / LAT Images