As has been said a large town preferably with an
>>>Admiral Nurse<<< is probably the best choice for ongoing treatment. Large towns will have better scanning equipment available.
As regards diagnosis you will first have to obtain UK residency so that you can be registered at a GP, the next problem may well be getting the person to come out of denial and agree to be referred to a memory clinic.
I think the time scale then depends not only on the clinic but on how the person presents themselves, my local clinic has 6 month or 1yr recalls for most people but for my wife it was every 3 months from Autumn 2009 to Autumn 2011 after which I used to phone the consultant's secretary if I had problems.
It took 4 weeks from referral with a CT scan and MRI to diagnose MCI, in summer 2011 it took a further MRI and SPECT scan to reach a diagnosis of severe degree LBD.
There seems to be an increasing tendency for memory clinics to discharge people after a few appoints (maybe only one) and wait for them to be referred again if the GP detects new problems.
As has also been said the partial introduction of the Care Act 2014 in April is going to radically change things, also in my area (Greater Manchester) the health (NHS) and care (LA) aspects are being combined and will come under the complete control of the GMC (Greater Manchester Council) and 10 LAs. No idea what the outcome will be. Other areas
may follow suit.