In the U.K. until what power can an electrical motor start directly???

Hi, in my opinion it will depend of the network that the motor is already connected, if you have enough available power to run the motor at seven times its nominal current per 2 or 3 second it will be fine, but you need to assure that there aren't other systems running at the same time otherwise you will have a blackout in the main breaker. Remember that kind of starting device are to induction motors and you can use this kind of auxiliary system when you want, normally over 5 kilowatts you will think in one auxiliary device, but again it will depend of your system, you need to make a calculus.

Well, conductor size and supply capacity are two big factors. Get enough supply capacity and enough conductor cross-sectional area and anything is possible. Sadly, the economics of doing so get in the way.