I have only ever been refused Class D crossing once, about three years ago by Brize Norton as they had an air display of some sort at the time, which is fair enough.
An ATCO friend of mine has often said that the quality of RT received, with its competence implications, has a lot to do with the granting of Class D airspace crossings (in addition to the usual controller workload and traffic density.) If you sound confident with a clearly stated route and set of intentions you are far more likely to be cleared through.
Use any pneumonic that helps you - variations on PHACER are the most common. A standard call for me would normally be:
A/C: "Brize Zone, XXXX, request zone crossing N - S"
ATC: "XXXX, Brize Zone, Pass your details"
A/C: "XXXX is a T67 Firefly, 2 POB, 5nm North of (VRP) squarking XXXX, Heading 182, FL40, VFR Navex, Routing Direct VRP to VRP, Estimate zone boundary at XX, request zone crossing at FL40"
ATC: "XXXX squark IDENT"
A/C: "Squarking IDENT XXXX"
ATC: "XXXX Identified, Flight Information Service, cleared cross the Brize Zone at FL40, report clear of the zone"
plaa343