Historically, most railroads throughout the world have had classification systems for their locomotives. Including in the United States, where steam locomotives were typically custom built for the various railroads. Diesel locomotives normally were standard models, with model designations from the manufacturers which became familiar to railfans in the USA. And most of the USA railroads eventually adopted the manufacturer models as the official locomotive classes.

In the European countries, each with a long history of nationalisation, railroad classification systems continued in use for diesel and electric locomotives, and multiple unit equipment. Although British Rail became privatised, with the formation of numerous Train Operating Companies, the British Rail classification system basically remains in universal use.

British locomotives were assigned 2 digit classification numbers, diesel below 70 and electric above 70. Multiple unit trains were assigned 3 digit classification numbers, diesel multiple units in the 100's and 200's, and electric multiple units in the 300's 400's and 500's. The fleet numbers consisted of the class number, followed by a space and 3 digits. For a total of 5 digits for locomotives and 6 digits for multiple unit trains.

The overwhelming number of British passenger trains are multiple unit, with a phasing out of most of the traditional locomotive hauled passenger trains. Traditional locomotives throughout Britain and the rest of Europe, electric and diesel, have cabs at both ends. Many longer distance trains in Britain now have dedicated power cars at the ends, similar to Amtrak's Acela trains. These power cars normally are semi permanently coupled to the trains, unlike traditional locomotives.

British Rail classes (Wikipedia)
Further detailed information.