I wouldn't do it cause it was their responsibility to manage the records.
I have some sympathy for your predicament, but not full sympathy, as given the length of time since you moved Flying Schools you should have sorted this out long ago. (I put this in mainly as a warning to other students).
To be valid all exams must be passed within an 18 month time frame so, if it is your earlier exams that are missing then you would only need to 'resit' those. If it is the later ones then the complete set would need to be sat again.
If you did in fact pass the full set of seven exams then this pass will be valid for two years from the date of the last exam (until May 2015) for Licence Issue - why did you wait until two weeks before your own deadline to follow this up?
Especially as you approached the end of your Flying Training, did your current school not keep pressing you for your exam results?
An Examiner may not conduct your Test unless you can prove that you have completed everything that is required for Licence Issue, and your Flying School needs to be able to sign a form stating that you have completed
all required training (both theoretical and practical).
Your old Flying School may have arranged for you to sit, and to invigilate, your exams but it will be one individual approved Ground Examiner who will have marked your papers. They are required to keep records of exams they have marked for at least three years.
Ask the school who it was who marked your papers - you may need to provide dates and subjects - and contact them direct for your results.
Results used to be recorded on
YOUR PPL application form (why didn't you take this with you when you moved to London?). Now, with online applications, I am not sure how Ground Examiners record passes for applicants.
I was infact planning to go to Spain next week for a quick sunny week of flying to get my PPL
How would this have worked? A Flying School cannot put a candidate forward for Test unless they can state that all required training has been completed. Would you have taken your London School's records with you?