Moving house shouldn't mean your vaccn records go as long as you give your current GP the details of your previous GP.
Were you born in the UK?
If so, you should have had DTaP/IPV/Hib at birth and both doses of MMR by now. Chickenpox, you can tick that box if you've definitely had it. BCG etc... if you know you've had it, tick the box. Hep B, assume you haven't had it and they will probably check for prior immunity - if not you can request. Hep A is irrelevant. You should have had DTP/DTaP shortly after birth and the school leaver's one, and a tetanus booster at some point.
Only tick measles if you've had separate measles vaccns, otherwise it's with MMR.
I think the fact you've had it is more relevant than when you had it... but yea, I dunno. And I've never been asked for this stuff for work experience... you're only there a week or so.