First deliveries of the new car are expected in March 2009 and Nissan has applied for extra supply to meet demand.
Paul Willcox, managing director Nissan Motor (GB), said: “The dealer order line lit-up on April 2 with an unprecedented amount of orders being placed.
"This clearly demonstrates the UK’s passion for performance cars and the enthusiastic following that the GT-R has established.”
The GT-R's engine is built by hand which limits the amount of units that can be made to 1,000 per month at the Tochigi plant in Japan.
Willcox said: "We are now starting to negotiate vigorously with Nissan Europe to secure further volume from our production facility in Tochigi.
"This volume has to satisfy all global demands covering America, Asia and Europe and therefore it will be late May before we know if we have been successful in our request."
Pricing for the GT-R starts from £52,900 on-the-road and the supercar is available in three trim levels: base, premium edition and black edition.