http://www.nhs.uk/ServiceDirectories...ceType=Dentist
Skater, there are a number of Dentists who do nhs work in doncaster. If the link above doesn't work then just type in "nhs choices" into google and do a search on doncaster in the toolbar search facility (click on the dentist search option). There is also a phone number to ring if you are having difficulty getting nhs dentistry in the area.
An nhs dentist may not do cosmetic dentistry on your front teeth unless necessary (e.g. if you tooth is not broken or decayed). They are also limited in the types of materials they can use. However, from what you say, you probably just need a bit of cosmetic contouring on your lower teeth which should be very cheap whether nhs or private. As the top tooth is not a priority maybe it can wait until you have a bit more cash. It's ideal to try to keep your natural teeth rather than bother with veneers. Your natural teeth are usually stronger than anything other than gold. There can be some risks associated even with braces so make sure you ask about risks and future potential problems before you go ahead with any work (in the case of braces a small percentage of people end up with permanently wobbly teeth!). Also make sure you get a full quote before you start.
An Nhs dentist may do the work privately if they are not allowed to do it on the NHS. However, their prices for private work are often far lower than those of a non nhs practice.
I wouldn't mention anything about your nail file antics to the dentist. They should be qualified enough to make an assessment based based on the state your teeth are in now without you having to tell them the gory history.