Brooklands Museum plans to restore the finishing straight to how it looked in 1939 when the circuit was in its heyday.
The scheme includes removing a World War Two hangar from the track.
Chief executive Allan Winn said the grant would pay for higher building costs and removal of industrial waste.
In February 2015, the Heritage Lottery Fund provided £4.7m for the restoration.
Brooklands said it was confident supporters and donors would raise the remaining £200,000 needed.
The restored Grade II listed Wellington Hangar - which was used for the assembly of Wellington bombers in the 1940s and later for other industrial purposes - will become The Brooklands Aircraft Factory, where visitors will see how aircraft from biplanes to Concorde were designed, developed and built.
On Monday contractors began laying foundations for a new annexe, the Flight Shed, which will house active aircraft from the museum's collection, such as its Sopwith Camel and Hurricane.
Aircraft will be taken from the old hangar, before it is taken down in August.
Work would then begin to restore the final stretch of the race track to be used again for motoring and aviation activities.
Brooklands opened in 1907 and went on to make motoring history.
For its first 20 years, the racing circuit was the site of many land speed record attempts.
At the start of World War Two the site was given over to use by Vickers-Armstrongs and Hawker aircraft companies.
Work has started to rebuild the world's first purpose-built racing circuit following an additional £1m government grant.