Hi James,
The diff would be a 3.89 or a 3.63 or a 3.27.
If you have a speed GPS app on your phone;
Drive a constant speed like 60MPH for example and note RPM in 4th gear Without overdrive energised if fitted,
Goto http://www.mintylamb.co.uk/gearspeed/
Input your rear tyre size.
You can input one of the above ratio's or just select spitfire1500 or both GT6's.
Match your engine RPM to speed and you have found your diff.
If you cannot drive the car you will need to get under it
If under it, look for rubber doughnuts or any CV's.
Measure the rear track. Only useful if you have OEM wheels.
The above information will confirm your rear end if it is Triumph.
I don't think there is a quicker way?
PS. You could use your car speedo, but it could be inaccurate or out of calibration. Tacos are normally pretty good. Nice with refried beans. RPM gauge is normally believable.
3.27 is my preferred diff for a spit2500. Best for the motorway.
Cheers,
Iain.