I am pleased to read of your interest in vehicle index marks in Britain. Their use dates from 1903 and the original allocation was made, with a few exceptions, on the following basis.
The English and Welsh counties and county boroughs, as well as various areas administered on a county basis, were arranged in descending order of population according to the 1901 census, and issued with one code each in the order A (which inevitably went to London) to Y (Somerset), continuing with AA (Hampshire) as far as FP (Rutland).
Combinations containing S had been reserved for Scotland, and were allocated to counties in alphabetic sequence of name, followed by the burghs in alphabetic sequence.
Combinations using I were similarly allocated to the counties and cities of Ireland.
Most issuing authorities subsequently had need of extra codes and these were issued on a rather more random basis. In 1974 various marks were moved to different issuing offices, coincident with the opening of the Driver and Vehicle Licensing Centre in Swansea.
Most vehicles on the road today have a registration number containing a three-letter group in which the letters denoting the origin are the second and third of the group — the first being merely a prefix to the index mark proper. The full list of marks and their issuing authorities used to be published in the annual AA Members’ Handbook, but for the current list I have to refer to my daughter’s AA Junior Atlas of Britain!