The end cottage was certainly being used as a pub in the 1890's. There's a photo of it from 1891 in Ian Boumphrey's book Yesterday's West Wirral (part two).
You could try checking on Cheshire Tithe Maps to see if it was there in the 1840's or 50's. I'm sure someone on here will know more.
Here’s the White Lion pub at the bottom of Grange Hill in around 1967-68. As you can see, the place was having a bit of a Changing Rooms makeover! I take it this place has always just been a pub
I don't know how old it is, but I do remember visiting the Charles Dawson museum in West Kirby and being told that bodies washed up on the coast were taken there temporarily, as it had deep cellars that were cool. That would indicate it went back a fair bit, but how long, I don't know. Might be worth checking old maps of the area?
