Steve Gardner did a repair of a 10A Carroll & Meynell Variac and documented the whole process on his blog:
I recently purchased a used 10A Carroll & Meynell Variac from eBay for use in the lab, however the variac often caused the 32A B-curve MCB in the consumer unit to trip due to the high inrush current of the variac core. To prevent this from happening and to add a few additional features I created the soft start circuit outlined on this page.
The idea of the soft start circuit is to limit the inrush current whilst the variac core is first magnetising. There are many ways to achieve this and most involve adding some form of resistive element in series with the transformer to prevent the transformer appearing as a very low impedance to the mains AC supply.
The method used in this project was to use a high power resistor in series with the transformer to limit the current. Once the current has settled, the resistor is shorted out by a relay to then allow the full load current of the variac to be drawn from the mains.
More details at SDG Electronics.
Check out the video after the break.