The oldest I can find is Thomas Taylor's map of Bidston in 1665, part of which you can see below. The map is oriented with west at the top. Bidston Hall is clearly marked, as is the Church. To the right (ie north) of the Hall you can see a large field named as Hall Paddock, in the centre of which is a rocky outcrop with a clear depiction of the cave drawn on it. The artist has even thoughtfully labelled it as "A cave" (written with a 'u' in place of the letter 'v', as was normal in the 17th century) to eliminate any doubt. This doesn't prove whether the cave is natural or man-made, but it at least shows it's of some age.
It's not really a map, but a set of survey plans covering the Wirral estates that ultimately belonged to the Vyner Family. The main areas covered are Bidston, Wallasey Village, Poulton-cum-Seacombe, Moreton and Saughall Massie, with a few odd fields elsewhere. The originals are (or were) at Cheshire Record Office, but they're not keen on producing them, preferring you to use a set of colour photocopies instead. Wirral Archives also have a set of the copies, but they're a bit hard to read in places as whoever did the copying hasn't been able to get the original pages completely flat.
