Romeo Fox,
Yes, both the company's you list are recognized by the CAA, to provide Certified APC (Assessment of Previous Competence) courses, for the purpose of having EU 805/2011 ATCO licences recognised. (I work for neither, by the way).
In one case, they have tailored the course to the ratings you need Certified. Once you get the Cert, you then proceed to Unit Training etc...
You could take a chance, get the certificate, then look for a job (very risky), or have a prospective ANSP take you on, on the proviso you get the cert,...however that might be paid for, (by you or the ANSP).
To find out the cost, contact the companies directly, it's not cheap. You could fund the course yourself, but I know of at least one ANSP who are paying the cost to get badly needed controllers from outside the UK on the payroll.
But I agree, none of this excuses the CAA for not recognising the licences of legitimately qualified ICAO trained controllers.
PM me if you wish.
Rocky.