Cex.io will have the same problem as most other UK based services, their banking will be somewhere else in Europe which means waiting several days.

Coinbase is the only major service with faster payments which means depositing in a couple of hours instead.

If you choose P2P instead of an exchange you'll be able to use faster payments as it's between individuals. Back in the day I preferred https://bittylicious.com for P2P stuff but premiums over the market price can get excessive sometimes. Other times it can match exchange prices.