Cesspool/cesspit liability and safety

Amphibian

I have just discovered what I think may be an abandoned cesspit in the rear garden of my fairly newly purchased house, which I think is in a poor state of repair and is a collapse risk. If so this obviously needs to be dealt with promptly before it causes any damage. While digging in the garden there was a sudden, albeit it small collapse of soil in fairly close proximity to some old outside toilets. the soil appears to have simply disappeared leaving a depression about a foot across and a foot deep. I left the site immediately for safety reasons without further investigation.

Now I have several questions on this subject.

At the end of my garden is a block of old outside toilets, now sheds, there were two toilets, one for the neighbour's house and one for mine, the neighbour still owns their shed. If the cesspool was a shared pit for these toilets would responsibility for this pit lie with both of us, even though the toilets are no longer present? The pit appears to lie under my property; though it may extend under their property too.

Has anyone any idea how much it might cost to demolish and backfill such a pit? I am particularly concerned about access as I'm not sure it would be possible to get even a mini excavator to the site.

Is this the kind of work carried out by a general drains contractor or are their specialists in this kind of work?

About ten feet away from the collapse there is an inspection hatch, I have no idea if it is a drain inspection hatch or a lid onto the suspected cesspit, if the latter this would be a huge pit, should I look inside it or would that be an unacceptable risk?

If the previous owner knew this pit was present and failed to disclose it - she said she was unaware of any private drains on the property - might she be liable?