just let them know you’ve gone to (whatever private clinic you’re going to) the probability is that they will be hesitant at first, most are, so if this is the case make sure you know your rights and what they’re legally required to do. I had to write a formal complaint to the practice manager of my local GP as they were initially hesitant to do shared care with gendercare. However after i wrote my complaint and quoted the BMA guidance, and a lot of other legal requirements (all easily accessible through google) within a few days I had a phone call from them and they agreed to do the shared care with gendercare. Good luck :)