An ophthalmic optician or optometrist (same qualification, the name change happened about 6yrs ago) who works in a high st. practice is qualified to deal with this and should be able to help.
However not all optometrists feel confident dealing with young children.
If you can find one who is (and I'll run through what the examination should include) then they are the best person you have access to directly.
If you can't find one who is comfortable (and that might take a few phone calls) you should go to your G.P who will kost likely refer you to see an Orthoptist (an expert in child vision and eye muscle issues). An orthoptist, working alongside a Ophthalmologist (eye Dr) or, more likely, an Optometritst working in the hospital will check the child, diagnose issues and instigate traetment if required.
A high street optometrist should use an age appropiate vision test (for a child age 4 this should ideally be a Crowded LogMAR card (sometimes known as Glasgow Acuity Card or Keeler LogMAR card)).
They should also be performing a cycloplegic glasses check (one which uses eyedrops).
They'll also do some other tests to check whether the eyes are straight, the health of the eyes and whether the brain is using both eyes together.
They almost certainly shoudl be giving teh full prescription and insiting on FTW.
Partial or half prescriptions and part time wear (for almost all prescriptions) used to be standard practice but now our knowledge base has improved.
It's a quite long post but I wanted to give some info about which route to take and what you should expect along those paths.
If I have been unclear, please post again.