I am ten years older than you, and we moved to a different part of the country upon retiring, which hasn't made getting to know new people easier.
However, that said, I have noticed since my late forties, that the older we get, the harder it becomes to make friends, and the longer it takes. There are also "false starts" where it seems to get ages to get anywhere. But persevere - sooner or later you will find yourself getting to know one or two congenial people.
I would suggest you keep up with one or two of the "older" groups - I imagine that in a year or so, there will be more of your own age-group retiring and joining some of these activities.
But, please do make it firmly and politely clear to those "old" ones who are taking advantage of you, that this is just not on.
You are justified in pointing out that you are neither a taxi service, nor a messenger service, and that you are no richer than they. Say right out, that you cannot afford to pay for their coffee or lunch - you can only very occasionally afford to eat out yourself, and that if you drive them anywhere, they will need to pay the cost of the petrol.
This will soon stop them. Just because you are younger than they is no reason why you should oblige with these services.
Do British chemists no longer deliver to the elderly, housebound, or those who cannot walk far?
If you really want to be helpful, but I personally would hestitate to offer even this help, offer to help them check on the internet what services are available to those who cannot easily walk to the doctor's etc. in your area.
What about the female friends you had before you stopped working full-time? Is there no possibility of seeing some of them once in a while for a good natter?