Next day is next day delivery although sometimes drivers run out of time its just a fact of life unfortunately.
If you do not receive your goods next day pop a call to OcUK (0870 443 0880) and explain that your goods did not turn up on the right day after posting and then a claim can be made.
If it turns out City Link were in error and didnt honour their contract at the end of the claim wolla, a shipping refund.
Just takes a wee while for the claim to be done as the circumstances need to be investigated but if they did not attempt a delivery it is usually possible to get a successful claim.