jsd, I volunteered with Age Concern, as it was then, for about 10 years and only stopped because the funding for the scheme I was on ended. It was some years ago but I enjoyed volunteering with them. I didn't do hospital visiting, but I cannot see that would be as difficult as volunteering with the CAB.
The thing to remember is that many of the old people you visit will have some measure of dementia. The thing to do is join them. No, I do not mean develop dementia, but I looked after an aunt and uncle with dementia for a while and sometimes their misunderstandings of life around them led to some interesting conversations. My aunt always called the home manager 'the commandant' because he reminded her of the Colonel at one army base they had been stationed at so she was convinced that the care home was an army facility. I never tried to disabuse her of this belief and when discussing where she was living we always did it in military terms. It is easier to share their world rather than try to get them to live in our world.