Indeed I have - I've now had both my NATS and CAA medical, but just lost my licence with the CAA as ended up in hospital last week! Doh! At least I'm not starting at the college till July so will have it back then!
NATS medical takes between 1 hr and 1.5 hrs. CAA medical took a bit longer as there was more waiting around - more like 2 hours or so.
Hope that helps!