Please explain your situation. What happened and why do you want to test for ABO incompatibility?
If you are planning to go the legal way then yes the solicitor would need to write to your GP.
All the tests that were required to be done would have been done by your doctor. You may consult another doctor who may advice any further tests.
The doctor will do the test only if it is medically indicated. And according to what you have written your doctor does not think that there is a medical indication for the test. Therefore my advice to you would be to take a second opinion from another doctor in your location.
Please open a new question requesting me.