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Personally, I think a 3lb test curve rod is too heavy for most carp fishing in the UK, and the maximum you need is a 2.75lb tc.
A 6ft 3lb rod is going to feel like a broomstick, and is likely awful for most fishing, but heavy test curves are the fashion. In most cases test curves of 3lb plus are designed for casting long distance, not playing fish. A heavy test curve rod is NOT always the best for playing fish around snags, better to get a lighter more through action rod around 2lb.
For ages my stalking rod was a 9ft Browning Spinning rod, perfect for floater fishing, fishing the lift method while carp stalking, but when it was stolen I went to a Daiwa 1.5lb test curve 11ft 6in Pro Specialist, then an Avon rod. In fact I would say a barbel rod is perfect for a lot of carp fishing. I use mine for floater fishing now, or lift float, and always on one water where the carp go from single figures through to 20lb.
I have caught a number of carp on those lighter rods to over 20lb from near lilies and snags.
Have a look at twin tip ledger rods, one tip section should be your quiver tips, the other is a barbel or Avon tip. For carp fishing the barbel or Avon tip is fine.