All we know about this premises (possibly mainly used a an off licence) is an entry in the Ipswich journal in 1778:

Simon Maw, Grocer and Wine-maker, of Woodbridge, late in partnership with Robert Dudley, informs the public, that he is removed to the New House, opposite the Queen's Head Tavern, where he sells as usual, wholesale and retail, all articles in the Grocery. The very best home-made Wines and Raspberry Brandy, on the most reasonable terms.Ipswich Journal, 21 Mar 1778***

Since the Seckford Street Queen's Head seems never to have had any buildings opposite it, we can be confident that the Queen's Head referred to is the one in Cumberland Street.