You may prefer to wait until after the account is closed simply because they will send one perhaps 2 'final' bills (one may appear a month after closing account... they do this in case any straggling charges accrue if (for example) the phone had been used abroad just before closing the account.
It's probably just as easy to ring customer services to say you wish to cancel... why make a special trip to a shop ?
For future (and advice I've seen on HotUKdeals.com) it is sometimes worth asking for the PAC (porting authority code) which one uses to move the number to another network. That needs to be done in place of saying 'cancel the contract' (I made the mistake of saying 'cancel' and have had to chase Three via OFTEL to get the PAC to move my number), and on asking, the 'retentions' staff may offer a better deal as they see you are serious about going.
I was after a deal costing 4 or 5 quid less than what I'd been paying with Three. Unfortunately it was for a phone shown on Three-Clearance.co.uk (a refurbished Nokia) and the deal for 11 quid a month gave 500 min, 5000 texts, unlimited internet, but the phone was out of stock and they wouldn't offer anything close to 11 quid to attempt to keep me. If they could have done a SIM with the allowances and ignored the Nokia (and perhaps charged a couple of quid less for it being without a phone) I'd have jumped at it.
Even more galling after the hassle I had asking for the PAC a week or two back, was that others have been offered (when asking for their PAC) a different phone, 500 min, 5000 texts, 2000 '3 to 3' minutes and unlimited internet for 11 quid a month, in the weeks since I cancelled. So a real kick in the teeth as far as I was concerned.
Anyway I managed to get a deal with T-Mobile offering their 'Full Monty' for 16 quid a month (reduced from 31) giving unlimited minutes, texts and internet, and TopCashBack should give me the sum of 101 quid in a couple of months or so, taking the overall cost to under 8 quid a month.
I wish I'd used a cashback site before I got the contract with Three a year ago, as that would have saved me about a fiver a month on the effective cost. Sorry if this is too late for the contract for your DD, Parisbanana but we often learn how we might have done things after the event, don't we...