I kept my home dentist, but changed Drs (tbh, I then kept them for the next 3 years as I lived in the same vague area and never needed a home visit). The uni health service was more of a drop in service and not suitable for routine care
I'm just going into my 3rd year - always arranged my dentist's appointments for the Christmas and Summer holidays and stayed with my one at home.
With the doctor, if you've registered away but need to see a doctor at home, you can see them as a 'holiday patient' for up to 14 days, with a form to fill in at the start. However, I've actually ended up seeing my home doctor quite a lot and have never been asked to fill the form in. Don't know if that's just my surgery being a bit lax though!