I'll also try to be brief, but as people know, I tend to waffle on...
So just pick out the bits you want and ignore the rest. I don't mind.
Many "classes", or designs, have come and gone. Some didn't hang around long at all (the "Class 14", a six wheeled shunting/switching and short trip loco only survived just under five years!) whilst others seem to have been around for ever, like the "Class 20" which was built first in 1957 and they are still hard at work (47 years old!).
Until the 1960s there was no unified method to describe the various types of motive power on the national network "British Railways (BR)". Each region had its own ways of classifying locos. Take, for example, the design we now know as "Class 37". On the London Midland Region (LMR) they were known as "EE Type 3, 1750" - rather a mouthful and not very concise. The "EE" was an abrieviation for English Electric, the makers of the machine; "Type 3" was the broad power category (1500 - 2000 hp), whilst the final figures gave the engine's power rating.
Click the image to zoom in
Class 37, before the TOPS system.
The Eastern Region (ER) devised a very neat numerical identification code which it applied to diesel locos. Under this system a "Class 37" would be called "17/3"; the first figures representing the horsepower and the last being a code number for the manufacturers. Of course the Western (WR) had to be diferent. In true GW style they were known as the "D66XX" Class, this relating to the number series then applied to the locos.
As a prelude to this computerisation of its rolling stock records (as Tim mentioned TOPS) BR set about devising a new class system for its fleet. This appeared in 1968 and was extended in the early 70s to encompass the multiple unit (MU) stock. The broad divisions of this numerical classification are as follows:
01-13 - Diesel shunters
14-69 - Mainline diesel locos
70-77 - DC electric locos
80-92 - AC electric locos
97 - Departmental locos.
98 - Steam locos (then remaining)
100-199 - Diesel multiple units
201-210 - Diesel electric mu
220-254 - High speed/intercity diesel multiple units
301-399 - AC electric multiple units
401-499 - Southern region DC mu
501-599 - Other DC mu
920 - Departmental AC mu
930-935 - Departmental DC mu

This is the Class 01.
Unfortunaley there were many diesel designs that never made it into the TOPS era. These present a special arena for modellers, as sources of info are often scarce.
Some gaps were left in the system to be filled later (eg Classes 38, 56 & 58) and others were used by more than one design (eg. Class 05 had two completely different locos within it (one shunter made by Barclays and one made by Hunslet). Class 43 was originally a Co-Co loco made by "North British" and after these were all withdrawn by 1972, the number was used for the HST ("Intercity 125") powercars. Some locos received now power units and with them new numbers (eg. Class 21 became Class 29, Class 30 became Class 31, Class 48 became Class 47s, Class 47s are now being converted into Class 57s, and so on...
It is not easy.
Many locos over the years have recieved nicknames. Some are given in the Downloads section of UKTrainsim. This doesn't really help newbies or those from overseas as has been witnessed. Some call all Bullnose classes from English Electric (eg: Classes 23, 37, 40 & 55) deltics, but only the Class 55 is accurately referred to as a Deltic due to it's Napier Deltic power units, and the prototype was named DELTIC.
There are LOADS of manufacturers. Some built the whole unit, some just the power plant.
Click the image to zoom in
Manufacturers include BR themselves who fitted Class 24 and 25 and 44-46 with Sulzer engines. They fitted their Class 42 and 52 with Maybach engines. Birmingham Railway Carriage & Wagon, MetropolitainVickers, North British, Brush, Beyer Peacock, Barclay, Yorkshire Engine Co., Drewry, Ruston & Hornsby are just a few of the others.
Click the image to zoom in
A fairly concise account is written by Colin Marsden & Graham Fenn called "British Rail Main Line Diesel Locomotives" and another book "The Diesel Shunter" by Colin Marsden is also good. Also this site
http://www.therailwaycentre.com/Pages%2 ... 0list.html is great. Its also got something to do with Colin.
Good luck.
Click the image to zoom in