If you want to be absolutely certain that you've got the job out of the way, the most efficient way to get your passports renewed is to attend a passport office counter in person. You need to make an appointment first. (Phone 0870 521 0410 - Lines are open 24 hours per day). For a fee of �114 per passport you'll receive a guaranteed 'same day' service or you can opt for a guaranteed 'one week' service for a lower fee of �97.
The Post Office 'Check & Send' service is designated as a 'two week' service but this is
not guaranteed and you'd be unwise to rely upon it at this busy time of the year. Similarly, the standard postal service is designated as a '3 week' service but, again, it's not guaranteed.
http://www.ips.gov.uk/passport/fees.asp
Information about renewing adult passports can be found here:
http://www.ips.gov.uk/passport/apply-renewing. asp
If you need to renew a child's passport, see here:
http://www.ips.gov.uk/passport/apply-child.asp
Chris