P60s are not produced centrally, they are produced by individual employers. There is therefore some variation in when they arrive, but the last date on which an employer can hand you a P60 is 31 May - ie today.
You are entitled to a P60 IF you are employed as at the 5th April. If you left before this time you get a P45, you should not get a P60. Some payroll packages automatically spew out P60's when they shouldn't and are then sent out by a payroll officer, who should know better!!