I have been offered a job with a start date of 2nd of June which I accepted.I was told company would get in touch on 29th of May with details.I have not heard back from Company. What should I do.?
As they gave you a definite date, what you should have done is to contact them on the 30th (or late on the 29th) politely enquiring about the status of the offer. As you didn't do that, you're in a bit of a bind as you're now going to need to be at least slightly pushy about it.
Pick up the phone and try and get through to whoever made you the offer ASAP. If you don't have their direct number, phone the office and explain to whoever picks up the phone what the situation is. If you really can't do that, use whatever means of communication you do have.