The official line from recruitment is that unless you have all three ratings, don't bother applying.
The unofficial line is, that if you conact the unit manager at the relavant unit, they will assess their requirements against your potential.
It's not unknown for atcos to be employed this way in NATS, but it very much depends on the strength of backbone of the unit manager and how hard they are prepared to fight your cause.
Unfortunately, your postion is not strong, there are many "aerodrome only", rate chopped NATS cadets around, your advantage is that you've validated your rating. I hope that youve managed to pin down a job at the unit you validated at, if so, stay there and take up any opportunity to advance yourself - then look at NATS.
Otherwise you could consider Serco, or Highlands and Islands Airports Ltd - who will only give you sponsership for the approach procedural rating at some outpost youve never heard of, but you'd be well paid for it.
Good luck!