Is it possible to do a training contract part-time?

I’m not aware that it is possible to do a training contract as a part-time job, only that the Law Society does allow a training contract to be undertaken at the same time as a part-time/distance-learning LPC. As far as I know, there is no list of firms that offer such an arrangement, so probably the only way to find out if the firms of your choice offer or would consider offering the combination would be to ask them. Those students interested in such an arrangement should also be aware that many firms may not even know that they can offer it, and so there will be relatively few firms that do offer it.