As I understand it dentists are all private businesses that do some or all NHS work. I think the NHS should set up its own dental practices employing dentists directly on a salary. A good salary with promotion opportunities.
They could buy old Debenhams/Woolworths/etc sites that are still sitting empty after many years (so should be cheap). Turn the upper floors into flats for the staff (low rent) and ground floors for treatment space. I know there are difficulties with these conversations but they're not insurmountable.
Parking may be an issue on site but city centres always have car parks nearby and are well served by public transport. This plan would also bring more life back to the high street.
This plan may take years to come to fruition, buying sites, converting them etc. This time could be used to massively expand training new dentists.
The biggest hurdle I could see in this plan is one the screams of 'no money' (so shortsighted) and dentists unions might block it.