Ok, it doesn't happen only in the U.K.
I had a case about 2 years ago at HAM. I advised the controller that we had a pax that just collapsed and were requesting medics upon arrival. Landed and waited. And waited. We finally let the "normal" pax out. The ambulance finally arrived, more than 20' after block on. Asked as to why, the medics told us they were on another case. By then luckily our sick pax was back to live, thanks to the well trained and cool F/As.
As to the ATCOs advising to call our handling agent and to arrange with them, I humbly don't think it is NOT a good idea. There you are, as in our case, already in the approach, and one of the pilot has to "quit the flight" to try to rise the handling agent. Most of the time they are not in the office, too busy or just not interested. During this time the other pilot is taking clearances, flying the craft, changing frequencies, and is unable to configure the aircraft, not a very sound situation indeed.
So, now and in the future, I will be happy to be able to count on any assistance given by ATC, thanks guys
------------------
... cut my wings and I'll die ...