There's often far less potential conflict in the overhead of an aerodrome than when you're a few miles from the overhead when you are more likely to encounter departing or arriving traffic. Of course it all depends like some airfields have beacons for holding on the airfield itself or local traffic might be practising forced landings from the overhead.
But as 3wheels above says there is no reason why you can't ask for transit overhead.
The other suggestion is always have a plan B if they ask you to go round. Where I operate from if you say go from Nottingham to Skegness direct that will take you right over Cranwell and Coningsby. In the week Cranwell will always ask if you can climb to 3,500 feet - if you can't they will ask you to go round. So if it's a gin clear day I overfly at 3,500 feet or above (and get a Basic off Waddington). If the cloud base is lower then I plan to go round via Grantham and Boston which is not much further and quite scenic.
Happy Landings!