Easternstandard- we loved Royal Caribbean when the kids were younger- loads of activities for them and we loved the American slant to the food/entertainment
We also like Princess- they have a system where you can have food/drink delivered to you anywhere on the ship which is amazing after a day hiking mountains in Norway!
Celebrity are a slightly better version of Royal Caribbean and had an amazing cruise visiting the Baltic countries last year.
We’re not a fan of P&O at all, but they’re relatively cheap tho, have lots of sailings from UK and if you like all things British it may suit you.
MSC is very multicultural and has stunning ships, but has more limited included food options- not great unless you love pizza!
Not tried other lines but Emma cruises is the place to go to find out more- she has a YouTube video and website.
From British ports- other lines that go are Disney (££££!!) Cunard ( Quintessential British!) Norwegian ( similar vibe to RC) Fred Olsen (older ships but well liked British food) Ambassador (new company, older ships)
Upper end- Viking, Seabourn, Regeant (all ££££££££!!)