Sara, you have the responsibility to ensure that all your referees respond to the reference requests from easyJet. It will be up to you to keep chasing them (i.e. YOU phone them or YOU email them telling them to pull their fingers out and respond to the reference requests from easyJet).
If you do not ensure that your referees have responded within a certain period of time, easyJet reserves the right to terminate your contract. Therefore, you must make every effort YOURSELF to make sure that your referees respond in a timely manner.
I would suggest that you contact easyJet's recruitment department as you do seem to be very unsure of what is expected of you. You will be spending a lot of money on your airfare over to the UK and you don't want this to go to waste, so contact easyJet recruitment and tell them everything about your referees and employment history now and ask them if their is likely to be any problems.
Remember though, easyJet is regarded as a 'self help airline' so you have to do everything you can to ensure that you are able to obtain your airside pass ASAP - failure on your side can result in termination of contract.