You get a P60 from the employer you were working for at the end of the tax year. It is your summary of the tax paid in the year. You do not get a P60 from an employer that you had left during the course of the year.
When you leave a job, should be given a P45, which tells your new emploer about your tax code.
If a the new employer is not handed his part of your P45, he has to put you on the emergency code and inform the Inland Revenue, who will then get in touch with you.
If you have more than one job, it is usual for all your allowances to be given in a coding for one of them, with the other employers being told to deduct tax at the basic rate.
Your next step should be to get in touch with the tax office and get them to sort out your coding.
The ordinary "Emergency" code results in someone being treated as having the basic single allowance. So if that is how you are being taxed, and the basic single allowance is all you are entitled to, the figures will be coming out about right. (The emergency code is applied on a week by week basis, and not on the running totals from the start of the tax year.)