As Jof 1999 says, NATS are not the only source of UK ATC info. Try contacting any local airfields/airports and see if you can have a chat with someone there.
A lot of controllers start out as (lowly, but valuable) assistants and get onward training from their company. However, there is no guarantee that this offer will be available if you secure an ATCA position, it depends on what you can negotiate and/or what the company is prepared to offer. Training through from an assistant to a controller can take a while and some companies may not be prepared to make such a commitment when recruiting, especially if you've no prior ATC/aviation experience.
Also, a few glider pilots are connected to other areas of aviation, you may find someone at your local gliding club is an ex-controller.