I fly out of Sandtoft so can help with the Doncaster bit, Call them up on 126.225 about 15 mins or so before you are due to want to enter their class D airspace & request a "Zone Transit" After their reply, pass on your details requesting a zone transit & they will give you a Squawk & talk to you till you are clear. They usually approve & will give you a height so as not to interfere with any of their traffic.
I would assume this would be the same for any other "transits" but willing to be corrected.
Hope this helps.
Trev