Steven Falk who is Senior Keeper of Natural History, Warwickshire Museum, thinks that the tree with five large trunks is a lime tree of some sort with an old coppice stool, which is why it has several trunks. It is probably not more than 150 years old, because multi-stemmed trees always get a bigger basal girth than normal trunked ones. It is typically Small-leaved Lime that is encountered locally in woods like this, but the foliage looks too rounded, so there is a chance it may be Broad-leaved Lime (frequent in parks, but much scarcer as a woodland coppice stool).
I'll have to have several looks at this tree as it is so wonderful and maybe when it fruits, this may help a clearer identification. Mystery solved?