Hi Yvonne,
The only pub I can think of in West Street is now called The Old Punch House, but although I dont suppose it was the original name, the address is number 7 West Street, so it could possibly have been next door to the one you are looking for depending on the street numbering.
I have been told Ware had more pubs than any other town in England so there were obviously a lot more than there are now. Number 5 West Street was once The White Swan Inn so perhaps your pub could have been number 6 in the middle.
Best wishes, Linda.