If you're transferring the funds electronically, then you'll be tied to that provider's charges and rate so won't be able to shop around, i.e. you'll be limited in your choice of providers to do this for you.
If you're doing it by draft, be aware that UK bank branches have, in the past, been wary of drafts drawn on non-UK banks and have applied high charges.
Also, if the amount you are transferring is 'normal' for a retail transaction, then the differences in the rate may not justify ringing around to get the lowest.