we had this problem a couple of years ago
our man hole was in our back garden, a guy up the street had put an air filter (and lots of oil) down his sewer and it backed up to us.
sweetcorn and pink toilet papermache…..*shudder
we had all sorts of problems as anglian water didnt want responsibility as they claimed the council were responsible for all properties built after 1930, the council didnt want to know as it was now privately owned.
Luckily the lady up the road who was a council tenant called them out and they did the work with a massive pump/generator business….
In short, if the blocked bit is your responsibility you could be looking at a big bill for some blokes and a pumpy thing.