I have been in and out of Sandtoft many times. The CAS boundary cuts through the centre of the airfield, and leaving to the North and remaining beneath the CTA, you are out of CAS almost immediately. I have never had any issue with a controller doing this and have only ever called once airborne.
If leaving and wishing to route south or south west I would skirt the zone beneath the CTAs until a clearance is obtained, or conceivably I might telephone first in order to arrange a direct transit once airborne. However, I can't see that this could readily be agreed over the phone, since by the time one is airborne the situation may well have changed and any earlier approval may no longer be appropriate, thus necessitating remaining beneath the CTA until a new clearance has been obtained in which case why bother phoning in the first place!