Train security from London to Glasgow

You store your larger cases in specially designed spaces through the carriage and smaller bags on overhead shelves. You will be absolutely fine. I have used that route to Preston for more years than I can remember and have never remotely felt concerned.

In addition to the storage spots already mentioned, some train carriages are set up with some of the seats facing in opposite directions, the seats positioned back-to-back. In that case there is often room in the A-shaped space between pairs of back-to-back seats to store a reasonably-sized suitcase. I don't travel first class, so I don't know whether first-class carriages in the UK are ever set up that way.

You could book your seats so that they are near the end of a carriage, allowing you to see your bags more closely in the racks between carriages.
You could also get up and watch your bags at each stop, stretching your legs at the same time, if you feel you need to.
Just keep your personal bag/purse/daypack with you, not in the luggage rack.
You’ll be fine.

No-one is going to steal your luggage:) larger suitcases go in the luggage racks at the end of the carriage. Hang on to anything critical in a smaller bag that you can keep with you.

Nothing to worry about.

A You Tuber has made a video of the trip.

I've used trains in the UK with suitcases and never once felt concerned that my luggage was at risk of theft. The storage racks are not secure, they're simply open racks at the ends of some of the carriages for you to slot your luggage in. There are overhead racks but they are only suitable for smaller items and thus you can place items that you'll want to have sight of.

I have actually heard of someone taking someone else's case as the got off, and I like to be in view of my luggage. When booking, you can usually choose seats and luggage storage should be shown on the carriage map.

Apart from the luggage stacks at the end of the train cars there are also mid car luggage stacks. And yes some seats have the A space between seat pairs.
First class is also generally less busy than standard so there is inherently more room.

But there is also no need at all to be concerned about this. Intentional (as opposed to accidental) luggage theft is vanishingly rare.

If I saw someone checking the luggage racks at every stop, as well as you impeding those trying to alight and board (to collect and stow their bags), I would be watching you very closely indeed and potentially stereotyping you as a potential thief (of my luggage) or terrorist, under 'see it, say it, sort it', and taking the necessary action. That is on the basis of that it would be extremely unusual behaviour.

I have actually heard of someone taking someone else's case as the got off, and I like to be in view of my luggage.

Mistakes happen but it’s far more likely on airport carousels.

Just don’t be tempted to do what I saw an American family try- padlock bags to the storage container. When they got to York they couldn’t undo the padlock in time and ended up in Edinburgh.