The only information I have is from someone who wrote up a history for William Bate. It looks like it was taken from commercial directories for 1777 and 1781. The writeup says simply that he was "landord of the Blue Anchor in Truro" those years. So I don't know if that was for the pub in Helston or perhaps a different pub by the same name in Truro. He lived in Truro at the time. According to a commercial directory, the Bate & Conn Brewery was an entity in 1783. I haven't seen the directory entries though.
Thanks for the link to Historical Romance UK. I hadn't seen that site.
The Boscawen Family lived at Tregothnan, the seat of Viscount Falmouth.
In July 1857 the "Tregothnan Office" Truro, placed a notice advertising property in 6 Lots, To Let by Tender properties in the 'Borough of Truro', which included the Queen's Head an old established Inn in Lot 1 and the Blue Anchor Inn in Lot 2, with Shops, Dwelling Houses and Land.
The land in Lot 2 adjoined Lot 1
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Royal Cornwall Gazette, 14th March 1835 Household Furniture For Sale.
TO BE SOLD BY AUCTION, on Friday the 20th day of March instant, at Two o'clock in the Afternoon, at Mr. James Russell's, Anchor Inn, Truro, the following HOUSEHOLD ...
It didn't say
Blue Anchor.
1849
The Truro Benefit Club held their dinner in the Market Place ...
which afforded much satisfaction, was supplied by Mr. Daniell, of the Blue Anchor Inn, Truro.
1804
CORNWALL
TO BE SOLD By AUCTION,
In LOTS,
At the Red Lion Inn, in Truro, on Saturday the 29th Day of September instant, at Five o'Clock in Afternoon,
A MOST eligible ESTATE called TRENNICK, situate in the parish of St. Clement, within a mile of the town of Truro aforesaid ; comprising a neat and commodius Dwelling House, with suitable Offices, fit for the residence of a genteel family, now in the possession of
Mr William Bate, a Farm-House, with convenient Outhouses, and about 99 Acres of very rich Arable, Meadow, and Pasture Land, commanding a beautiful and extensive view of the River Fal, and the adjacent country.
The Premises are at present let in parcels to different tenants, for several terms.
...
... Messrs Foote and Karslake, Attornies, South Molton, Devon.
Dated September 1, 1804.