Adam/Choices
While you've got the right idea about getting involved in ATC before applying to NATS for a cadetship, you will piss a very large number of people off (who will invest money and a lot of their time in training you), if you do get an ATSA position and then in three years time, leave for a cadetship.
To be honest, the majority of NATS ATS Managers will not employ you if they think that's your intention.
However, if you apply and are succesful in getting an ATSA post at a non NATS airport, you'll almost certainly find that they run their own in house training scheme for ATCOs, and you'd be wise to mention your desire to do this with them as opposed to a NATS cadetship.
Under those circumstances, you'd probably serve 2 - 3 years as an ATSA, apply for the ATCO training, get all your ratings, and 3 years or so after validating as an ATCO, you'd be in a strong position to review your options career wise, (especially if you wanted to defect to NATS).
You should also bear in mind that although a NATS cadetship is probably the best training you can get, there's no guarantee you'll be streamlined for the aerodrome and approach radar ratings, the majority of NATS cadets (I think) end up as area ATCOS.
I know of a few airports that are looking for atsa's, and also run their own atco training schemes, but they do have a 3 year bonding scheme after the atco validation and would not consider anyone who was looking to run off for a cadetship.
Good luck.
