Renewing your UK Passport
A lot of countries won’t let you in if your passport is within 6 months of expiry. If you have a UK passport, you can renew it up to 9 months before it expires and when its renewed it includes the unexpired period of the previous passport in the validity time.
Because making it easy doesn’t appear to be an option for Her Majesty’s Passport Office, you can either fill out the application form online, which they then post you to check and send back with all the supporting information or you can do it via the post office.
All the information is contained on the Passport Renewal Information page. They say it takes 3 weeks at a minimum but I’d allow double that since you have to get the form, fill it out and then send it or make an appointment with the post office.
I’d suggest that as soon as you’re 9 months out from expiry you’d be best renewing it. That way you know it’s done.