HayleyK - what do you actually want? You could insist on a battery of extremely invasive tests to rule out all possible causes of your son's hypotonia (would probably need to go to a specialist children's hospital or specialist wing of a large London hospital), or you could have physiotherapy, OT and speech therapy to deal with the symptoms and wait a while before you do further tests (many conditions rule themselves out over time, and often, however many tests you do, you never find a cause). If all you really want is to treat the symptoms at the present time, and there's no indication that your son is likely to have anything potentially life threatening wrong with him, then I don't see what would be wrong with the place you've been referred to: I'm sure they will have seen other children with hypotonia and hypermobility before.
Having said that, I know nothing of the place you mention, although it sounds similar to other units throughout the country that bring all children's OT, PT, and similar services under one roof. So long as the people you see specialise in paediatric care, you are likely to be seeing people with sufficient expertise to help your son.
My son is also hypotonic and hypermobile and now he's 4, having received PT and speech therapy, regular reviews from a paediatrician and some assistance from an OT, he has been reviewed by a neuromuscular specialist and we will be seeing a geneticist. Prior to now, we haven't gone down that route, because a diagnosis was unlikely to make any difference to his treatment and we didn't want to put him through the trauma of testing for a needle in a haystack. As he has got older, most possible conditions have ruled themselves out - certainly the more serious ones. We are now pretty much left with hypermobility syndrome/Ehlers-Danlos syndrome and some exceptionally rare myopathy (which no-one thinks is likely). Or, of course, no diagnosis - and continued OT and PT as and when required to deal with the symptoms.
Having said that, there is no right and wrong answer to what you should be doing for your son. And if our son had been affected in other ways besides having the hypotonia and hypermobility (eg cognitive deficits, obvious muscle weakness in addition to the low tone, breathing problems, difficulty swallowing food, failure to thrive), we wouldn't have been so inclined to wait and see.
Good luck in whatever you decide!
By the way, have you looked on the ivillage hypotonia board (messageboards.ivillage.com/iv-ppchdhypoton)? There are loads of people on there with hypotonic children, many of whom have had all the tests going and masses of therapy. You would get loads of helpful advice and support from people on there.