The noise on your video is electrical intermittent contact so usually a bad phase wire contact or motor wire.
The motor wire from the hub often has a two part connector with in 30cm of the hub often located on the front fork RHS. Make sure it is fully pushed home, each part should have a small raised black arrow marked for alignment and may need a torch to see properly. Disconnect it (a strong tug needed) and reconnect it pushing home fully.
Also a poor phase wire connection can be the cause to find these follow the motor cable all the way to the controller box, inside you will find the metal controller and all the wiring at one end. The thick Blue, Green and Yellow wires are the motor phase wires check the bullet connectors are properly pushed together, the bullet connectors often can get warm and sometimes they can become loose and need gently crimping together to tighten up again. Give the wires a tug to make sure there is not a poor or broken wire.
Other the fault if the LED display goes out/switches off, is a poor battery contact or faulty controller. But most often a wire fault is the cause.
I don't know of any e bike shops in London to recommend but sure there must be on or two, Woosh bikes are good in dealing with faults they are in Southend so a bit far out.
There are some London forum members so one of them might be able to recommend someone.