Selling a comic collection in the UK

I've got a decent sized comic collection I'm looking to sell on as I've recently become a dad, and I'd like to pay down some debts so I can give my son and any future siblings the best start possible.

I'm based in the UK, and I've got lots of long boxes of things going back to the 80s and earlier - a complete run of the New Teen Titans, Spawn up through issue 150 or so, loads of Flash and Green Lantern issues, etc.

It's a substantial amount so the question is: how might you go about selling such a large collection to get best value and how would you organise actually physically getting it to the buyer?