It is unknown when the Blue Whale was established, but it did exist in 1897 (704) and it appears to be in the same location as The Eagle was from 1796 to at least 1940. Given that Sophie Baker wanted Barnabas Collins to take her back there (704), it would appear its reputation in 1897 was not much better than that of The Eagle in 1795. By the late 1960s it was a much more reputable place.
The 45-rpm recording of Quentin's Theme had as its B-side Number One at 'The Blue Whale', the background music played at the bar. (London Records - HLD10283 - 1969 - The Charles Randolph Grean Sounde)
In 3, a phone booth is seen in the Blue Whale, however after that point, all phone conversations are made with the payphone on the left wall.