How to change the lamp holders in my Dimplex Cheriton electric fire?

You talk of lamp holders plural - suggesting at least two.

One lamp holder might have failed but it would be a very big coincidence for two to fail at the same time.

It would be reasonable to assume a common failure that affects both lamps - a fuse you don't know about - a wiring problem - a switch broken or in the wrong position. It needs to be looked into.

As for your question - could you do it yourself - I would guess very unlikely but not impossible.

Good Luck...
November 2015