Yes you can have a partial denture on the NHS under Band 3 charges. Whether you can find an NHS dentist is another matter though; and then there are dentists who do mixed Private & NHS treatment-which makes it complicated further.
My DH is a dentist - half private/half NHS. Yes - they can be done. Although, as with anything, you get what you pay for. The NHS standard will be reasonable and fit for purpose though (according to him)
Samnickless - just seen your thread re the partial denture. May I ask why you ask as I am in the same boat. Desperately trying to come to terms with the idea at the moment, but I think it's my only option.