Starting new job if still employed...

[smesh]

Im currently in full-time employment and I've been offered another full-time job. Can I start my new job before I've technically ceased working for my old employer ?

Because I currently work flexi-time I've got 24 hours owed to me, plus 5 days leave carried over from last year, and if I start the new job at the begining of June, I will be owed 4 days leave for this year... in total 12 days.

Instead of wasting those 12 days at home waiting to start my new job, is there anything to stop me working for the new company during those 12 days ? My old employer isn't any worse off because its paid holiday owed to me anyway, Im better off because I'm effectively being paid twice for those 12 days, my new employer doesn't have to wait a month for me to work my notice and the tax man is still getting his share out of both salaries...

Three years ago my employer before this one I'm leaving now wouldn't let me do it when I ask them, but they never gave a reason ... I figured they were just being arsey and didn't see why I should be paid twice for the same period of time..