Nice to see the picture of this one, good find.
It's interesting to see the way it is built - almost as an appendage to the front of the house. Perhaps this is not so unusual when you consider that it started out as a 'Beer House'.
Also, the Victorians had a way for creating shops - they simply built them in the small front garden of many a larger house, so that you sold in the front and lived in the back. Just a variation of living over the shop. Quite a few examples still exsist if you look for them. Examples can be seen in Oxton Rd at the top of Tetbury Street.
There were a couple of posts about this place in April 2012, under the 'Chat: Wirral Pubs Past & Present' section, as follows -
"If I remember there use to be a Pub on Borough Road that was called the Rose and Thistle just pass the old pet shop opposite the old fire station, then we had the Music hall by Charing Cross.
"I think the Rose and Thistle was in the part of Borough Road between Nelson st and Collingwood st but on the other side of the road.
There's an old pic of it in one of Ian Boumphreys books
"Just had a quick look at the large scale OS Map, and it was indeed almost opposite the end of Nelson St at 93 Borough Rd (south side). I'd say about 20 feet away to the west from where the flyover joins the level road. On the map it is marked 'BH' which actually stands for 'Beer House' which is a bit different to 'PH' for Public House. Possibly this part of the map was never updated before this and adjoining buildings were demolished in the first phase of works for the Borough Rd section of the Tunnel Flyover in about 1967."
The attached photo gives some idea where the pub was. The centre line of the road for the flyover is just inches away from where the old kerbstones outside the pub was. So, coming about 20 feet back from the foot of the flyover would put its location in the foreground of this picture.