Ok, so now I get it:

Hugh's father John was the half brother of Philip Shimmin (1801-94) of Corvalley Farm, Ballaugh. So Hugh and my ancestor Philip Shimmin (1828-1921) - who married Sarah Teare and married again in Australia - was Hugh's first cousin. So I was right, young Philip Teare Shimmin who lived with Hugh in Liverpool's Rodney Street was his 1st cousin (once removed?).

Keith and I then share the common ancestor Hugh Shimmin (1752-1814) of Douglas.