According to the Museum of Liverpool Life website, large numbers of the flint tools used by our hunter-gatherer forebears have been found in this area. Apparently there are fantastic views of the estuary from here - it's the highest point in the Wirral so perhaps it had good views in prehistory too. And perhaps its elevation explains the folklore connected with it - if you remember, when Thor struck his hammer there was lightning: a high spot like this would be bound to attract thunderbolts. Or maybe Thor's axe Mjollnir really is buried here.
The place is consequently rumoured to have been an altar on which those nasty Vikings offered sacrifices to Thor. Or maybe they really did - the rock is very red: maybe it's stained with all the blood. The woods and common nearby have a spooky reputation too. But this obviously doesn't put off the local Morris dancers, who use this as a Mayday dawn dancing spot.
From its description, the place does rather sound like Alderley Edge to me, with its red sandstone and 'edgey' quality.
(gleaned from all over the internet, and Hole's 'Traditions and Customs of Cheshire' 1937)
THE GREAT STONE OF THOR.— The following statement will not be without interest to your archaeological readers. In November, 1877, I called attention in the columns of N & Q.s to this venerable relic of prehistoric antiquity, probably of Danish origin, which exists at Thursaston (Thor-stane-ton), Cheshire, about eight miles from Birkenhead, and which, from its secluded position, has almost entirely escaped notice. I then stated my apprehensions that the advance of modern improvements would be likely to lay it out for building villas, for which the site is admirably adapted.
A commission of inquiry was sent down, which communicated with the Corporation of Birkenhead, being the nearest market town. It happened, fortunately, that the article in" N. & Q." had been seen and noticed by several members of this Corporation, who drew the attention of the commissioner to the desirability of preserving the monument. The result has been that not only will the monument be preserved, but sixty acres of. the surrounding land are to be set apart for a public park. The gigantic rock altar, with its beautiful natural amphitheatre, will thus be kept intact for ages yet to come. This circumstance, I think, affords encouragement to those who interest themselves in the preservation of our remnants of antiquity. J. A. PICTON.