Any claim against the council would be assessed by the courts on the 'balance of probabilities'. If he (and his legal team) can only show that his medical problems COULD have been caused by mould he won't get a penny (and he'll probably be left with a multi-thousand pound bill for legal costs). Similarly showing that it's QUITE likely that the mould caused his problems would be insufficient. He would need to show that, based upon the balance of probabilities, the MOST likely cause of his hospitalisation was contact with mould (and also that, based upon the balance of probabilities, it was the mould in his home - rather than elsewhere - that was responsible).
Further, he'd also need to show that the council had been NEGLIGENT in dealing with (or failing to deal with) the mould problem. If the council stated that he'd never told them about the mould (and he'd got no copies of letters to prove that he had done so) the court might rule that it was unreasonable to expect a council to fix a problem which it had not even been made aware of.
Your friend will definitely need legal representation if he's thinking of taking action against the council. However, before he even contacts a solicitor (which will start clocking the bills up) he should try to find out whether anyone (such as his hospital consultant) would be prepared to stand up in court and state that exposure to mould was the MOST likely cause of his problems, rather than just a POSSIBLE cause. Without such a favourable expert opinion he'll be wasting both his time and his money if he proceeds any further.
Chris