Do I have any rights regarding regular overtime?

[Cheeseandtomatotoasties]

I work part time in retail and have been doing an extra 10 or so hours a week overtime for well over a year, doing one job in particular.

I've heard that sometimes overtime can form part of your contract if it's a regular thing over a fair period of time. The reason I ask is because my overtime has now suddenly been taken away and those extra hours, which I've come to rely on, have gone towards new starters part time hours.

Can my Manager do this?

You’ll have to look at your contract and company overtime policy.
Often overtime is not guaranteed, so yes can be stopped with no formal notice.