I photographed this car at the SeeRed meeting at Donington Park in September 2006 where it may have competed in the GT Class in the Sports Racing Masters race, but it isn't listed as a competitor in the programme of the event.
It looks like a Jaguar E-Type Lightweight, of which 12 were built in 1963/64. Checking through the chassis numbers of the Lightweight cars (850658 to 850669) I find that only two were built with a fixed-head body - 850662, the Lindner/Nocker car, and 850663, the Lumsden/Sargent car - and this car most closely resembles 850662, which had the registration number 4868 WK. I've found photographs of replicas of the Lindner/Nocker car, however, and it appears that 5497 WK may be one of these. Peter Lindner, incidentally, was killed driving his E-Type in an accident at Montlhéry in 1964, and the car's race number was 16. The car was wrecked, but not rebuilt until 2011 - so it can't have been the car I photographed in 2006. In 2014 Jaguar announced that they were to build a further 6 Lightweights, and I've seen photographs of the first of these, but I've not yet seen that all 6 have been completed.