Should I get my booking fee back?

[Chelseaocean]

I’m sure it’s likely in the t&cs but I paid for an event which then got cancelled and the booking and admin fee weren’t refunded.

yes

If they cancel,yes you should get it all back.

Usually but you need to provide more details

Citizens advice say you might not get it back.
https://www.citizensadvice.org.uk/consumer/event-tickets/event-tickets/getting-a-refund-on-an-event-ticket/
You’ll probably only get the face value of the ticket back - the amount printed on it. Some sellers might refund postage if, for example, the event is cancelled before the tickets are sent. If you had to pay any booking or card fees, you might not get those back.