Hello again, all.
We have a friend who works for Medway council. He had a look at the archives and found nothing at all- there are no pipes, private or public sewers being recorded. As such, this is still a mystery.
It is not incredibly deep and I have no fear of going in there- I can't see it being unsafe.
From the inside, the walls slope upwards and inwards at the top where the square access hole rises upwards from the middle. Again, the walls are perfectly smooth and curve upwards into a domed roof.
There are no dates or any markings at all on the cast iron cover. Our friend agreed with me that the brickwork of the square entrance is relatively modern. He also said that older access holes would have had rungs or steps built into them whereas more modern ones didn't. This is due to more modern health and safety rules and that access would be gained by a tripod over the hole and a rope lowering one downwards.
It still seems that my only option is to digdownwards and keep you all updated to my findings. I appreciate the offers of help but understandably I am reluctant to invite strangers round my house to ponder over a hole in my garden! Thanks for those offers though!