I am by no means an authority but as far as I know NATS will not sponsor anyone for a visa. There are more than enough people in the UK and EU that are already eligible to work in the UK so there are more than enough applicants. If you are eligible to live and work in the UK already then NATS will accept your application. Sorry I cant say anything more positive for you.
As I said I am not an authority so someone else may know a way round things.