Hi. Can anyone advise as to what size modern tyres I can use to replace the existing originals as these have all seen better days.

For the standard 3-1/2x12in 500 wheel, use 125R (or SR)12 tyres--Pirrelli still can supply this size. If you have early (594cc) 126 wheels fitted which were 4in wide, go up to 135R (or SR) 12 tyres

Hi thanks for the info. When I put those sizes through EBay it comes up with motorbike tyres. Are they the same as I need?

NO--car and motor-bike tyres are different. The construction of a motor-bike tyre allows for the fact that for a fair percentage of its life it will be running on the side-wall (when cornering)--hopefully, a tyre on a car will not be doing this! Middle Barton Garage can supply the tyres that you need.