The so-called 'Hermit's Cave' in both Bluebell Wood, Handsworth Wood and Redhouse Park are ice houses or ice boxes. In Bluebell Wood there is actually two ice houses: one is a circular hole in the ground resembling a conventional brick-walled water well about two metres (2 yards) in diameter - the other is the colloquially known hermit cave, as recalled by Master Ingram from his nefarious youth, that cave is no more than a substantial youth-sized hole dug out of the sandstone bank slope to the River Tame...and it does indeed resemble a cave. As tourist spots the Bluebell Wood ice houses would be a subjective choice to consider an actual visit...a bit like the Tate or the tat Modern: not much to see!
In days of olde the landed gentry sent forth their servants to dig deep'ish holes in the ground, and in this ground they would collect and deposit and make in the winter months, ICE. Ice that has been frozen multiple times over multiple years in a freeze/thaw/freeze cycle is quite resilient to actually thawing out completely at the warmer times of the year - think the resilience of the frozen tundra and/or glaciers to thawing and ice houses and ice boxes are of that ilk. An ice house in use was visually portrayed in the television series of 'Cranford', when 'Lady Ludlow' played by the delicious, Francesca Annis arranged a summer picnic for the village and at this picnic the villagers consumed (in the height of summer) ice cream made from m'lady's very own ice box that resembled a coal-shed...artistic licence perhaps?
Access to the ice-house and ice-box, Bluebell Wood, Handsworth Wood: Drive along Parkside Road then turn into Woodend (a small cul-de-sac). Park car and walk towards River Tame. Walk downstream for 100 metres and there is the 'Hermit Cave' on your side of the river. The ice hole is situated on the small path that runs through the small Bluebell Wood. If you are parked on Woodend, take the path through the wood and the ice hole is 30 metres on your left.
Just to reiterate, save for childhood memories and/or historical curiosity, there is not much to see of these Handsworth Wood landed-gentry relics!