I can't say for certain it was demolished because of the Tunnel, but it seems most likely. The inn itself was on the corner of Bridge St and Park St. The number was 203/205.
Attachments: Viewing Permissions May Apply. Click Me
205 was enumerated for the 1911 census and it's recorded having 5 rooms, this could have been the living quarters while 203 was classed as the business premises.
Like many other pubs in the area, the Sun Inn was used on occasions for inquests by Birkenhead Coroner, Mr Churton.
The 1864 snippet from the Cheshire Observer (if you can't see it) has Joshua Jones, Sun Inn, Bridge St, in possession of a greyhound that wasn't his, the bench expressed he wasn't aware it belonged to the complainant.
Edited by bert1 (11th Oct 2016 11:01am)
God help us,
Don't send Jesus,
This is no place for children.