We had a drain just outside our front gate, always flooding. Council and local housing wouldn't take responsibility. Any time it rained heavily we'd literally have a swimming pool in our front garden. The council said the drain system was sinking and it was too expensive to fix.
So my husband phoned the council one day (he was really peed off), told them he had been carrying our baby daughter out of the front garden and had slipped. Next day, a bloke was round jetting the drain to clear it. Two days after that, two men dug up the drain, put a bigger one there and re-routed the pipes to the main pipe which was a mere two metres away in our neighbour's garden. Took them less than half a day to do it - hardly "expensive". Not had a problem since.
During this time we took photos and video evidence in case we did actually need to prove the problem in case of an accident. It's just a shame that sometimes, lying is the only way to get the council off their arse!
Make sure you take LOTS of pictures, even video on your mobile phone. No doubt they will be trying to cover their tracks in case you make a claim. B*stards.