We have moved into a three storey town house, is it a legal requirement for all internal doors to have door closures fitted.

Not any more, Building Regulations used to require many internal doors to be so fitted, but removed the requirement as in reality these doors usually ended up with the closer removed or a wedge put in place.

The doors to the stair will (or should be) fire doors, but only where a fire door separates an integral garage from the accommodation is a self closer required.

(This all assumes the premises are occupied as a single family unit and is not being used as a House of Multiple Occupation)

Further to AB posting check out “Main changes in the 2006 edition – Appendix B of Approved Document B (fire safety) volume 1: Dwellinghouses also page 30 diagram 10.