Generally easier getting them to come to you. Initial City Link won't (really) deal with casual passing trade - business only.
Your best bet, for items that aren't particularly valuable, is to go to eBay and look for a cheap courier - search "cheap courier". You'll generally find one for £5-£8.
It's a bit of a scam - they promise a big carrier (UPS, Fedex, etc) to shift 100,000 parcels a month without being too worried about a one-hour pick up slot, so get a dirt cheap rate - £3-£4 probably. They advertise on eBay. After a couple of months of only managing 1,000 per month UPS shut them down for not managing promised levels of business; they take their 5k profit; we've taken our £5 courier services.
Beware; your contract is with the third party, so the insurance is essentially valueless - they won't pay up without a struggle, and they're likely to disappear. On the other hand as the delivery is outsourced to UPS, you can check delivery online etc. etc., so the odds of losing a parcel is slight. Just don't pay the extra for insurance...
Thanks for the helpful tips. Another angle on this story is that we're charging the parcel to an existing account and we have the option of Fedex or UPS. Sounds like longlaner's suggestion is what we'll need to go with.