Had no joy about this in pub section so am trying it here.
clicky
no dont think there was a pub but there was an off licsence on the corner of rodney & helena street just about remember it I grew up there its been a house for a number of years now .
There was an Off-License run by Jock Grey, he had two daughters who both went to the Convent School Holt Hill, on a recent visit to Birkenhead i noticed that the shop had been reverted to a house, as we lived at the top end of Rodney St it was the nearest and well used Beer seller.
I've checked the cencus from 1881 to 1911, and the premises at No.59 were occupied by the Owen family during this time. Mr Owen is described as a 'Grocer Shop Keeper' or a 'Provision Dealer'. During that time his wife and children assisted him in the trade. It seems reasonable to assume that this was a corner shop with the family living above the buisness. Most of the neighbours seem to have had some sort of employment in shipbuilding. I've also checked the other corners of Rodney St, and they would appear to be just housing. Unfortunately, the cencus does not normally indicate the use of the premises, only the occupation of the occupants.
From the photo on the Birkenhead Vigilence topic, the house has obviously had an extensive makeover, with the external brickwork being replaced fairly recently. It looks like the front door has shifted to the side of the house, so now it is the only front door in Helena St. Its original position was almost certainly on the corner, judging by the coping stone, thus making this a true corner shop in times past. The old OS maps also show it without a front garden wall, thus giving room to put their wares on display.
In the Birkenhead Vigilence article on Beer Houses, it can be seen that the possibility exsisted for any premises to sell or even brew and sell beer for the payment of a fee and not need to appear on a cencus or OS map.
The Licence Registers, as far back as they go (ie to 1880), confirm that 59 Rodney Street was licensed for beer off-sales, until February 1963 when it acquired a full off-sales licence covering wines and spirits as well. The first recorded licencee was James Owen, who held it until August 1912 when it was transferred to his daughter Catherine. In 1923 she married William Gray (who I presume hailed from Scotland?) who was still the licence-holder in 1963, having bought the business in 1945. The Registers confirm that there were no other licensed premises in Rodney Street.