The light bulb alarm on the dash only comes on when the brakes are applied and then goes off when the brake pedal is released. Both rear lights fail to illuminate but the high one on the tail gate works OK. I've already tried replacing the switch on the brake pedal. Can anyone recommend what to check next ?

You don't say that you have tried new bulbs; have you?

All single and double filament bulbs have been replaced along with the brake switch as per the video, 

Pull one of the rear clusters out and check for voltage at the contacts on the bulb holder. Use a weight, krooklock or spouse to hold the brake pedal down.

 

Multimeter, if you have one, or a £2-£10 circuit tester from Amazon.
https://www.amazon.co.uk/Circuit-Testers/b?ie=UTF8&node=1938316031

 

Just in case, bulbs should be P21W or 382 model, single filament. Similar to these.

https://www.halfords.com/motoring/bulbs/382-p21w-car-bulb-plus-25-percent-longer-life-halfords-twin-pack-717565.html