A slight update.
Taken from the Freddie O'Connor books - A pub On Every Corner - out of print since the late 1990s.
No mention of the High Park, but has this on the Peacock Inn.
Peacock Inn
Probably the earliest inn of three that were all close to the summit of Park Road. This sketch dates from 1820(*) when it would have been part of a small hamlet in the countryside to the East of the road. Situated a little South of the present High Park PH near High Park Street, High Park was the highest point of Toxteth Park and the Peacock Inn was probably a former lodge of the park, apparently built c1635. The premises were also known as the High Park Coffee House but had been demolished by the 1870's as was the High Park Tavern, situated facing the Peacock between what would become Wellington Road and Greil Street, both cleared to make way for the ever increasing spread of terraced streets. The Brookfield family ran the Peacock from the 1820's to the 1870's.
(*)Small sketch, but I can't be arse scanning it at this time of night.
If you want it tomorrow, let me know.