Hi there
I had to do one of these for Virgin. I managed to get all my dates from looking at various things like P45, tax forms, etc and also contacting old employers (this one works best). After all, you only need to put the dates down to the best of your ability, and if you get them slightly wrong its nothing serious because you have only done it to the best of your knowledge and that is what you are legally signing to confirm.
Hope that helps!