It's not beyond the realms of possibility to get a job as an ATSA having got the ADI rating, but you are up against a huge amount of competition from existing employees at airports who are the usual suspects when it comes to filling existing ATSA vacancies.
Most, but not all, regional airports advertise and recruit from within or will invite external applicants who have already applied speculatively if there isn't enough internal interest.
It's worth enquiring with every non NATS airport to see if they would employ you at a nominal rate (£1 per year or so) just to allow you to validate the rating within a fixed period of time.
You may even be able to negotiate subsequent employment as part of the deal if you are succesful. I know that will be at your expense but it would prove how genuine you really are. This has been done elsewhere in the past but is very rare these days.
To be frank with you, the reason you are not a very marketable commodity at the moment is because you only have the ADI/ADV rating, without stating the totally obvious you need at least the APS and preferably the APP rating as well.
I know that involves a huge investment on your behalf but, if you were taken on as an ATSA, you would be on a relatively poor salary for at least 18 - 24 months before you would be considered (with no solid guarantee) for further training at most units.
If you invested in the APS rating I would wager that you'd regain the costs much sooner by being more employable and thereby commanding a much higher salary.
Alternatively, have you actually applied to NATS or Eurocontrol?
Anyway, the best of luck to you and let us know how you get on.