Upvote:9
So I've figured it out. If you lose a British passport in the UK and require a new one ASAP get the first appointment at IPS that you can and then request the same-day service in person.
If the passport you lost is a biometric one (issued in 2008 onwards) they will be able to do it -- if it's not, then you'll have to wait for a week. Your travel, or other circumstances don't seem to matter.