The T1 set a lap time of 1:10.6 - seven seconds quicker than the Koenigsegg CCX which held the previous record.
However the rules state a car is only allowed on the leader board if it can drive over a speed bump.
Top Gear’s makers decided the Caparo T1 would be unable to do this and removed it from the top of the leader board.
Caparo now claims the production car will be fitted with an adjustable suspension and will therefore be eligible for the Power Lap.
Angad Paul, chief executive officer of Caparo, said: 'We certainly hope that the Caparo T1 is given another chance by Top Gear to take its rightful place at the top of the leader board; even if they put a speed bump on the track we are confident of our success.
The vehicle’s designer, Ben Scott-Geddes added: 'The model we supplied to Top Gear was one of our final engineering vehicles without adjustable ride height and electronic active driver control systems which are standard on our production models.
'When driver’s select the "road" setting, the car is more tractable in slower speed conditions and the ride height is fully adjustable to bring the car up to 90mm clearance, making it more than capable of driving over speed bumps.'
But the Caparo could face stiff opposition if another car, the Ultima GTR720, gets a chance at the Power Lap leader board.
British supercar manufacturer Ultima recently celebrated its 15th anniversary by smashing the lap record on the Top Gear test track.
The Ultima used was fully road legal, with standard tyres, and was even driven to the test track.
Ultima’s director, Richard Marlow, said the company has approached Top Gear on a number of occasions to let the Stig take the wheel of the GTR but has been repeatedly turned down.
They used their own benchmark driver to get the independent figure of 1:12.8, two seconds off the Caparo.
But Mr Marlow wouldn’t rule out further attempts at an even quicker lap with their more powerful and faster GTR800 variant.