​Looks like a nice pub. Fullers. Close to the old Fuller Brewery in Chiswick and just off the Thames.
I will report with real pictures.

A popular and upmarket country pub. Doesn't overplay the Nelson connection. Cosy (low beams, open fires) and large rear patio/dining.  Website outdated but here:
http://thenelsonbrightwell.co.uk/ thenelsonbrightwell.co.uk/

Provided by Mike Cuming, (52-59) who lives in Sydney and has been hosted here and donated his old school cap for their display.  He probably had to explain many times that whilst he went to Nelson's old school, it wasn't at the same time.  Branded a Brewery Hotel, established just 36 years after the Battle of Trafalgar, in 1841, it can be found here:
https://www.lordnelsonbrewery.com/ 
Pictured Mike with Archie Fraser, who sadly passed December 2024.