When did you change and when are you going?
Sorry for the delay.
This is a difficult situation. You should really change your passport over forthwith. It is probably going to be a risk because your driving licence is at a different address.
However, if you do then you would potentially be without it.
The truth is that passports are turned around now usually within a week. They will tell you that it will take ages and ages but that is not the reality.
An alternative though is to go up to the passport office and get it done within a day. That causes inconvenience obviously but it can be done.