I know that there are diagrams with the cars listed but I can't tell whether the left or right side of the diagram is the "start" of the train. In other words, are the cars numbered from the engine to the station or the other way around? Thanks.
Usually A is the carriage behind the engine, but if your train is returning from a dead-end station (as opposed to a through-station), then on the return journey carriage A will be at the back. In other words, the train could have an engine at both ends, so it would be difficult to predict where any particular carriage will be, you’ll just have to take a chance.
and virtually no trains running today actually have separate engines (locomotives) at the front or the back.
They are almost all diesel multiple units with the engines under the carriages, or electric with motors under the carriages, or a few but growing number of hybrids which use a variety of fuels in a small hybrid converter in the middle of the train.
To be able to answer your question, if an answer is possible, please share the train company and place you will board and your destination.
For example, in the usual configuration (subject to alteration because of circumstances, when an announcement will be made) of Avanti West Coast the First Class end with the higher letters is at the London end (London Euston), and the low letters are at the northern standard class end.
Different companies and different equipment may be different.
Always assume the train plan you have in your head is not correct, only trust the diagrams on that platform for that train And the displays on each train car.
And many British train employees speak a version of English, you can often understand some of what they are saying :)