If you pick up the voltages going to the front turn signal lights, they will "repeat" exactly what the the turn signals do...if the turn signals are continuously on as running lights at night, or as DRLS, they side repeaters will stay on as well, but they will also flash as needed on turns. They will not come on with braking. I believe that on side repeaters I have seen, such as on European delivery Volvos and MBs that are then used here, the side repeaters will be on solid most of the time, and flash as needed on turns. Would that be a problem for the MOT compliance?
If there is a concern with adding the additional current draw of the side repeaters to the front turn signal circuit, you could use the front turn signal bulb voltages to energize relays that would in turn switch voltage on an added dedicated fused supply circuit from the battery to the repeaters. You can get the relays at any auto parts store. The circuit positive could be connected right to the battery via a fuse in an in-line holder. No current will be drawn unless the turn signals are actually turned on, so you should not need to route the power through the ignition switch to prevent draining the battery with the car not running.
I would think you would have more of a problem with driving a left hand drive vehicle over there, even if it that was MOT compliant. On the few occasions where i have driven a large American LHD car on roads in places where the British drive to the left rule is followed, it was kind of unnerving going around curves, hard to see the oncoming traffic when you are way over toward the shoulder of the road vs being closer to the middle of the road, especially on narrow roads that are common in the UK, and everyone drives like they are in a cross country rally.