Maximum legal size?

In Australia, the maximum legal size wheel in most states is generally
no larger than 1" more diameter and width than the largest standard
wheels fitted to a variant of the same car.

Now you might have fun persuading them that since some Mokes had 13" x
5.5" wheels, you should be allowed to fit 14" x 6.5" wheels to your 1961
Mini 850....

To go larger than this you need to get engineering approval. The UK
probably has some sort of similar guidelines which you should be able to
get hold of from your local vehicle registry office.

    Maximum size for racing?

Read the class rules...

    Maximum size for building a special to show off big wheels and tyres?

The critical dimensions are usually the diameter of the rear wheel,
which must clear the trailing arm pivot and the width of the front
wheel, which must clear everything in all states of steering lock and
suspension compression.