"agent thinks tax office will only go back 5 or 6 years for p60 stuff."
HMRC can actually provide your tax details for a lot longer. But you can't just go to your normal tax office, as they will need to access their archives
Check out this link
http://www.hmrc.gov.uk/industrial-compensation/
You can make a record retrieval request back to 1996/97 (which is when they introduced self assessment) or a Subject Access Request which goes back a lot further.
My husband is a tax inspector and said that whilst these requests are rare HMRC can and do provide this data - you just might need to be patient and make sure you go to the right person or office. You should also be prepared to have to push it a bit.
They'll also be more helpful if your tax affairs are in order. Which I guess they will be if you are solely PAYE.
good luck.