The categories of people who can get free (or reduced cost) dental treatment are shown on pages 62 to 67 of this leaflet:
http://www.nhs.uk/Healthcosts/Documents/DH_4138953%5B1%5D.pdf
You'll see that none of the main categories apply to you but that people who've got an HC2 certificate get free treatment and those with an HC3 certificate pay reduced costs. Those certificates are provided to people who can prove that they're on a low income (with no access to large amounts of savings or other capital), regardless of any other circumstances.
To apply for an HC2 (or HC3) you have to fill in an HC1:
http://www.nhsbsa.nhs.uk/HealthCosts/Documents/HealthCosts/HC1_April_2016.pdf