I had quite a few big gaps in mine and they were happy with a personal referee of good standing to verify that I was where I said I was....just the time I took off between modular courses and gardening leave between previous jobs etc.
What does "unable to check" mean? Are the companies you worked for out of business? Maybe your referee has moved on?
The tax office (I think somebody said) is a good place to go - they might be able to verify your employment. Alternatively, maybe organise better and/or current referees at you previous places of employment.
AFAIK, they aren't allowed to discriminate agains you and deny you an airside pass if you have had over a certain number of previous jobs!!!
Good luck!