luggage on British trains

There are no luggage rules. You are responsible for your luggage. You carry you luggage onto the train and store in appropriate places generally in an open bin near the entrance to the coach. Done it for decades with no problem. And this is true in nearly all in Europe for trains. Generally, not always, there are narrow over head racks that will hold a day bag or a small carryon near your seat.

Make sure you can lift it easily yourself. Depending on the type of train, there may be racks at both ends of the carriage for large luggage and you can put smaller stuff on overhead racks. Keep valuables with you. Don’t put your case on an empty seat because the train might get busy later and then people will glare passive aggressively at you rather than asking you to move it. Don’t block the aisles. Be prepared to move quickly when departing the train. There will usually be an announcement when the train is approaching each station, which gives you the chance to gather your luggage and prepare to get off.

No more than three items, do not obstruct doorways, gangways or corridors, and you normally need to be able to manage your luggage without additional help and not cause delay to trains are the main rules.

If you need anything more specific give more details.

Just adding to the "keep valuables with you" advice -- if you leave the car to go to the lavatory or for any other reason, take your day pack with you. Thieves may assume you have valuables in there such as laptop or tablet. It only takes a moment for a professional thief to unzip and grab the item, leaving your pack looking completely undisturbed. (This happened to a friend of mine some years ago.)

There are no luggage rules. You are responsible for your luggage.

This is only partly true. In the UK there are rules about how much luggage you can take but nobody knows or applies them (including the rail network and TOC staff) so there may as well be none,

You are responsible for your luggage and you lift it on and off. There is no checking in. You will need to put big bags into the spaces at the end of the carriage. Do not be tempted to chain them to the racks. I saw an Australian try this at York trying to get off a train from Edinburgh to London, and London is where he ended up.

It was tragic and quite funny at the same time.

Just adding to the "keep valuables with you" advice -- if you leave the car to go to the lavatory or for any other reason, take your day pack with you

In real life nobody does this. Reality is 1) some train toilets are so small you won’t get in there with a back pack 2) nearly always there will be other passengers - use the words “would you mind watching my bag” then go and do your business 3) if your bag has been taken someone will have seen it or it will be on the CCTV which is ubiquitous and 4) the culprit and your bag will still be on the train so call or get someone to call the British Transport Police 5) I wouldn’t want to put my bag on the floor of a train toilet. 6) if you don’t leave something on your seat someone may sit there

The advice to make sure each person can handle his/her own bags is essential. I know that many of you kind and thoughtful husbands feel that you should carry your wife's bags for her. This is not the time for that! You need to be able to make it down the aisle and out the door with your luggage without blocking everything for everyone else.

I have frequently encountered these "sherpa husbands" who are trying to be kind and handle 3 large roller bags and carry ons while the wife does a small carry on bag. It doesn't work. They end up being very unkind to everyone else on the train as they try to make 2-3 trips down the aisle toward the door of the train with the luggage and try to unload it all themselves.

You can check the various train operating company's website to see their rules but as already stated don't think they are ever enforced. They might be if you tried to board with say four large cases.
For example LNER state allowance is one large suit case ,one carry on case and one small handbag per passenger