I am presently researching the possibility of getting a special seating chair made. It will be made from block foam with a vinyl cover and a base of plywood reinforced with steel.

Both the foam and cover meet the required flammability testing. Therefore would the chair as a complete need to be tested? If so is this testing done at one central location or are there various test centres as I am located north west and finally are the costs standard to perform these tests?

I would suggest you go to FIRA at http://www.fira.co.uk/ they will have the answer. If it is domestic try http://www.firesafe.org.uk/furniture-and-furnishings-fire-safety-regulations-19881989-and-1993/.