I think that loneliness falls into 2 types, those who have loneliness thrust upon them and those for whom it is something inside.
By those who have loneliness thrust upon them I am thinking of carers, one eloquently described on the radio today that as a carer for her mother with dementia, she has become more and more housebound, as the dementia got worse and it became more and more difficult for her to meet friends as she could not get out and they could not visit her at home because her mother couldn't cope with strangers. Physically disabled people unable to get out of their homes unaided are in a similar circumstance.
For this group, most have social networks they can recreate or groups they can go back to, what is needed is a regular weekly time when they can be provided with reliable regular respite care, so that they can get out and meet friends or do whatever they wish.
For many of the other lonely, even if they were given 'prescriptions' to go to a club or day centre, they would not go, they lack the confidence or feel too awkward or embarrassed to go anywhere like that by themselves and if they do go, it is a disaster, they creep in the back, hide in a corner no-one notices them so they slide out and go home and never go back.
What Lynne and others need to do, is find a way of knowing who these people are. Could health visitors, doctors or charities for the aged like Age UK pass on contacts? Then make contact with them in advance, giving them a lift, or getting someone to come with them the first time and then keep a eye on them to make sure they are drawn into the group and do not exclude themselves. Ring them before the next meeting and repeat the experience, until they have the confidence to come in the door alone by their own choice.
For those lonely because of the loss of a loved one, Many have social lives outside the home, it is inside, both the individual and the home that loneliness lies and I am not sure one can do much for that other than offer sympathy.