It is not necessary to transfer your domain name to another provider in order to use their hosting service.
Simply apply the domain nameservers related to your hosting account (as supplied by your hosting service provider) to your domain name and this will point your domain name to your external hosting account.
If in the event you do want to fully transfer the domain name to another provider (thus making them responsible for your domain renewals) please see the following page for assistance with transfer costs and charges:
https://www.uk-cheapest.co.uk/domain-charges.php