There are opportunities that the NHS/private sector can not offer. The whole Naval package - AT, professional and personal development, travel etc.
If you go down the Commando route you will be the dentist to a Commando unit, act as part of the Medical Team (in action you would be helping out the doctor with life saving and stabilization to move people on to the next part of the Medvac chain) and as is seen by the guys on deployment you may find yourself the first and possibly only dentist the local will ever see. I spoke to a guy who was part of the RM group who went to North Iraq back in the 90s. He was treating hundreds of people who needed proper dental care to save lives, infected gums etc. He did education for the locals and emergency care. He said it made all the work and grief worth while as he eased the pain of the these people.
At sea there are some permanent jobs, the big ships, but you will normally jumping from ship to ship to do your thing. You will get to know loads of people and if you pick the ships right you can do all their visits as well.
The majority of your work will be ashore in the Dental Surgeries doing preventative work. You will make sure that everyone coming through is dental fit to deploy. If your ship is 1000nm at a sea and someone has a dental problem they are going to get the LMA patching them up at best. You get none of the pressure of NHS targets and costs. The Navy will help you professionally and if you make the Navy your full time career they will support you. If you decided that you are going to do a few years then move on you will make friendships that last for life, skills that will help you and if you miss it that much join the RNR.
If you are still interested get along to your AFCO and speak to them. They will get you on touch with the Medical recruiters and they will help you.