There is a Hinkley Triumph dealer in Ipswich called Lings but its not really worth taking even a modern Triumph there! Most 'new' Triumph owners take them to other dealers in other counties or other non-Triumph dealers in Ipswich.
As for Meriden Triumphs, the only one I know of around here is in Felixtowe (about 15 miles away) called T8 Triumph Spares. They are appointment only for visiting but you can contact them at their web site -
http://www.t8ts.co.uk - I cannot comment on their service or anything as I have not used them yet, the 5TA being my first classic Trumpet (always been a BSA man but don't tell anyone round here!) I'm sure there are others and I will find them in time.