The 2015 edition of the Pevsner guide to Suffolk East by James Bettley in the Woodbridge entry (p599-600) has a section on Theatre Street where it says: "No 11 housed the Free Grammar School of 1577, but may previously have been a guildhall. At one end beneath the jetty are the heads of a doorway and three windows of an early C16 shop, with a carved beam, also C16 but from elsewhere, inserted later to create a thoroughfare; this is supported on vigorously carved corbels. On the r. of the opening a dragon post, showing that the building was originally jettied at this end."

This is clearly a revision from the second edition written by Pevsner himself which said: "No 11 above the present archway four former window heads, four-centred arches. To the r. a little carved angel from the corner post." The window heads can be seen in the following photograph.

So far, this is the only mention I have seen for the possible site of a Gildhall in Woodbridge. However it is likely there was one (or more) because Section 32 (by Peter Northeast) of An Historical Atlas of Suffolk (see Sources) has the following statement: "The majority of parishes in the Western half of Suffolk certainly had gilds; most parishes in the north-east of the county also had gilds, but conspicuously few in the south-east. In this latter area most parishes seem to have depended on certain centrally-placed gilds, principally at Framlingham, Kelsale and Woodbrige."

The Historic England listing information for No 11 is here.

Here is a view of the archway:
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The carvings to the left and right appear to be angels. As Pevsner, in 1961, only mentioned the one on the right I wonder if the one on the left is more recent? They are shown here:
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The building is not adjacent to the church but it is only a short walk (procession) from it. A wider view of the building and the name of it is here:
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Underneath the archway is evidence of older windows:
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The extract(s) below are taken from one or more of the following articles in PSIAH (see the Sources page for details of how to access).

Morley, C., 1926, A check-list of the sacred buildings of Suffolk, to which are added Gilds. XIX Part 2, 168-211.

Redstone, V. B., 1904, Chapels, Chantries and Gilds in Suffolk. XII Part 1, 1-87. Has abstracts of 39 gild certificates, 18 in Bury (presumably the 1389 returns). Also details of Ipswich Corpus Christi gild.

Redstone, V. B., 1937. IV. Extracts from wills and other material, showing the history of Suffolk churches, chantries and guilds (Appendix to article published in Proceedings Vol XII). XXIII Part 1, 50-78.
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For information on buildings mentioned in the Pevsner guide to Suffolk in this location see pevsnersuffolk.co.uk