I don't know where you live, but check if there's a branch of U3A University of the Third Age) in your area. It's a nationwide organisation for retired people which allows them to get together and share their knowledge in their specific interests. They normally have a General Meeting with a guest speaker once a month, with all the sub groups meeting in members houses or church halls on a monthly basis. The one I belong to has lots of different groups. such as Ornithology, Bridge, Italian, History Lovers, Gardening, Science, Antiques, French, Walking, Current Affairs, Music, Computer Users, Digital Photography, Painting, Opera, etc. If you Google U3A, the website will probably help you find your nearest branch.
The National Trust (if you're a member) also have local groups which meet regularly to arrange outings, etc.
Also look on the notice board of your local library. It will often have details of local organisations you can join, or those who are looking for volunteers.
If you enjoy reading, your library may also run a Book Club where members join together once a month to read a specific book and discuss it together. Your library will probably have details of Adult Education Classes available in your area and if you are on benefits you may be able to attend these free, or at reduced rates.
Could you set up a Neighbourhood Watch group in your street? That might help neighbours get together and help you make new social friends.
And as another person has suggested, your local church is a good place to try and find out about local activities and perhaps make new friends.