In the UK, who decides the price of an eye test, the government or the opticians?

Question

Also, is it possible to have varifocal contact lenses?

Answer 1

The optician. Different opticians have different prices.

You can get varifocal contact lenses.

Answer 2

For those who qualify for NHS tests, (Under 16, 16-18 in full time education, over 60, on certain benefits, having certain medical conditions...) there is no charge at all. The fee paid by the government to the opticain for this is generally somewhat less than opticians set for private examinations, which can vary (unless they are operating a loss-leader policy or other discount as a business tactic)

Varifocal contact lenses do exist, but the success rate is not high, though those who do get on with them tend to consider them wonderful.
Monovision, correcting one contact lens for distance and one for reading remains almost as successful as any of the high-tech (and expensive) options. Only trials of the various types can determine what might actually suit.