Matty,
Although i’m not a carp angler, i could recommend a couple of places. I live in Failsworth and we have a place on our doorstep (Daisy Nook Country Park) which has Crime Lake and Sammy’s Basin. The basin has some big double figure carp but you get hassled too much. Crime Lake has Carp over 20lb ad i beleive a couple of thirties or so i’ve been told. If you become a member of the club (about £25 for a year) you can fish the private pegs which are gated off for members only. There have been some financial problems with the club running it – Medlock Anglers but i’m sure this has been resolved as i’ve seen a few “bivvie boys” loading up their cars lately. Have a walk round and i’m sure you’ll get the info you need.
There’s also Roman Lakes (lakes road, marple) where i learned to fish as a kid which has loads of carp over 20lb and a few thirties. It also has a cafe and easy parking.
If you want to go a bit further then Brookside has weekend permits available on the specimen lake (can’t remember the name of the lake).
There’s probably loads more but as i said, i’m not a carp angler.
Hope this helps, good luck.