I am assuming the manhole was only built for pedestrian traffic and not upgraded when the use of land was changed (i.e car traffic)?
If you can find the old cover photograph it and check the rating falkirk-mark is correct to suggest that it may have not been up to the job. If you can't find the old cover ask for the original recipt.
Now might be a good time to check if you have legal cover on your insurance, phone them on Monday and see what they say with regard to how you are covered for third party liability. I don't see this as being any different from your wall falling over and damaging a neighbours car.
Have you discussed this with whoever is being asked to meet the other third of the costs?
At the end of the day you have to live next door to these people do you want a war?