LNER and Avanti West Coast offer the most amount of free food/drink in 1st. up to full (small) meals and alcohol.

Cross Country, Transpennine Express, East Midlands Railway (only on trains to/from London), First Great Western (Inter city to/from London) also offer free drinks (not alcohol) and snacks.

Transport For Wales offer a paid restaurant quality meal on some Cardiff - Manchester/Holyhead trains.

1st class lounges at various stations are available, they are run by the specific company and only available to people with 1st class tickets for their trains so make sure to add a qualifying journey to your pass in case they ask for it.

Look at the company websites for details on their offerings.

Thank you!

Great, so I can look at www.nationalrail.co.uk whicht train companies are serving the different routes. Or is there any better website?

What about specials like e. g. steam trains which are possible to use with interrail?

Any idea how hotels in UK like it, when you book a room for 2 adults and then bring two small children (2 and 5) extra? (problem is, when you search for 2+2, you most of the time get expensive hotels with two rooms we do not need, as our children sleep in the same bed with us...)

LNER offer the best first class I would say. They’re also the logical choice of operator for London-Edinburgh anyway.

Do a fare search on the LNER website, and you will see the results marked with Dine, Dish, or Deli next to the first class fares for each train. Try to pick a Dine train, for the best meal service (although be warned that they have been known downgrade).

UK first class lounges are pleasant places to wait, and again LNER tend to be fairly decent and refurbished, but none of them are worth a special trip.

With any operator, expect slimmed-down menus at evenings and weekends, and possibly better service on the peak-time flagship services.

I’m not aware of any steam trains you can use with Interrail in the UK. There are some very scenic trips not to miss if you’re passing that way: The Settle-Carlisle line in England, and the West Highland line in Scotland. They’re regular timetabled services with diesel trains and stunning scenery. (Both second class only.)

Thank you. 
Are there different trains on the same route? For example a „dine“ train and later only a „deli“ train?

And how do I know if they serve me food when I only go part of the line? 

The trains are the same (well, the LNER on this route are). It’s just the menu that changes. You can see examples here: https://www.lner.co.uk/first-class-travel/menu/

I think the general rule is that if your journey is more than an hour, you’ll get food. Less than an hour, you might only get drinks. But the hospitality staff don’t check your ticket or ask where you’re travelling to, so they tend to just offer the menu to everyone.