Well, thats a pretty big question. As with commercial records the 5 biggest are always going to be the majors so you'd be looking at the likes of EMI, BMG and Warner. However, if you're looking to work with them going and knocking on the door isn't going to get you very far. You can of course submit music to them and if its excellent they may work with you but you may want to look at working with other (smaller) companies to get your foot in the door. There are numerous smaller libraries and you can find a complete list of the UK ones by looking at the PRS website (https://www.prsformusic.com/
Do your research though, some companies listed here are great and others are unlikely to get your music played anywhere so look into the companies before agreeing to do lots of work for them.