Have had all the carpets in my flat replaced over the past couple of years, each time used Collins Carpets, Tottenham High Road. Very happy with the result, and always surprised at reasonable charges. For a little extra, they will remove all old carpets and underlay and take to the dump. Collins (also known as Kusi) can be reached at 020 8493 0707.
I contacted Collins Carpets using the mobile number that's on the front of the shop (07956 383048). He came out the same day and fitted a carpet which we had already bought. He's a nice bloke, very professional and reasonably priced - definitely recommended.
He wouldn't take the old carpet away, but I guess that is because you have to book a slot in advance at the Council tip now, giving your details, and it's only allowed for householders. Any carpet fitter that does agree to do that may be taking the old carpet elsewhere...
Another issue is you need a waste Licence to take waste / Carpet etc. That's why so many get dumped in the Borough
Understand Only vans need to book a slot , these days
Reason you will see several Large SUV's taking rubbish away
M and L carpets on Crouch End Hill are really good and may not be as expensive as you'd think given their address!
I used Tapi in homebase, they were good no pressure.