skysight,
Just to add my opinion/experiences.
Competition for NATS is tough, but if you are the right person for the job, there is no reason why that should be a barrier, and as HD has stated you will have a guaranteed training position at a unit afterwards.
There are 3 colleges NATS, Global ( formerly ASTAC) at Gloucester and Resource (Cwmbran). The 2 'private' colleges both have their merits and are regulated by the CAA just as NATS are.
If you take the self funding route, take the time to visit both colleges. It is an expensive route and carries some personal risk.... Remember not everyone has the aptitude for the job, and completion of a course doe's not guarantee validation and a licence.
If you plumb for ADI (Aerodrome) only initially, with a view to a foot in the door somewhere, and further funded training. This is one option, but there are alot of unvalidated Tower only trainees looking for a foot in the door at the moment. If you are specific about where you want to be based this is something to consider.
On that note NATS ATCO's are a mobile grade, so you go where they tell you.
Starting as an ATCA (ATC assistant) is a great way to get a feel for the job and at some units, if you demonstrate the aptitude, its a great way to get your training fully funded (with a bond) with a training position afterwards.
Training at the unit to validation standard will vary greatly depending on the unit, how many trainees there are and how many instructors (OJTI's) there are and of course how fast you pick it up.
The time taken to validate your first rating could be anything from 3-4 months to over a year... Alot of variables.
You maybe required to have Aerodrome, Approach Procedural and Approach Surveillance (Radar) ratings to work at some units. Self funding you could expect little change from £50k.
Good luck... It's a great career.