This is an awful situation for you op 
Obviously, you cannot be held to blackmail by his threats, yet at the same time (in case he means it) you need to take the threats seriously.
So (maybe check with the Samaritans)) but I think the official advice on this one is to validate his feelings (acknowledge he is hurting) and tell him he needs to seek outside help. Tell him the relationship is no longer healthy for either of you and his wish to commit suicide is something that is a symptom of a bigger, deeper issue (ie none of should be dependent on one person for our existence) and he needs to seek outside support for it. Perhaps write down some numbers for him, eg Samaritans, gp etc, but do not get drawn in any further. Tell him gently that we are each responsible for our own happiness, that he ultimately wouldn't want you to stay with him not out of love but because of suicidal threats, and that he needs to take responsibility for his own MH. Also tell him that if at any point you feel he is going to harm himself then you feel it is within your rights to inform the emergency services, his family, his friends, his work colleagues etc, but that you won't be getting personally involved further than that. Obviously, do not get drawn in to a situation where you are alone with him and he has a knife or other weapon or dangerous substance. Protect yourself.
Again, check with the Samaritans but I believe the most dangerous time for this sort of threat is from the point of a break up until about six months afterwards. Speaking very generally, except in a very few cases, most of these situations resolve after this time without any actual suicide or self harm, and the person who threatens suicide accepts the end of the relationship.
Therefore op, it is very unhealthy for you still to be living with one another as it extends the agony for both of you. I know finances are stretched but could you possibly move out and sofa surf at friends' houses, until the end of August?