The Tamplins Ales advert looks like it might be giving directions to the Maltsters Arms. There was a Maltsters Arms in Montague Place which closed in 1960 according to the Closed Pubs website.
This thread is so dangerous to your time. Seeing that picture sent me down a rabbit hole trying to find out who Arthur H Cox & Co were to have such a grand building.
The most surprising thing about that photo is how old the balcony that sticks out from the building on the left is - I assumed it was some 70s/80s addition
Pictures of Worthing - https://historicengland.org.uk/images-books/archive/collections/photographs/usaaf-collection/#gallery-5-1 and Cissbury Ring - https://historicengland.org.uk/images-books/archive/collections/photographs/usaaf-collection/#gallery-5-2
Thanks for posting those. It shows those of us not old enough to remember the West Pier being open what a wonderful ornate structure it was and also what a great job they did restoring the only remaining structure on the prom.