Oxfordshire has a growing number of Pottery Painting Cafés, especially in towns beginning with W, where apparently they gather!
Typically these cafés offer a wide selection of blank semi-fired pottery items that you can decorate. They then glaze and fire the item for you, and you can pick it up around 7-10 days later. Some charge a studio fee, some don't, and the items usually range in price from inexpensive small things ("pocket money items") around £5 up to huge platters, vases or teapots costing £70.
Many cafés offer other art materials, including Decopatch (sticking decorative papers onto figures or furniture), block printing onto cloth, mosaics, and the popular printing babies' hand or footprints onto pottery. Some also take imprints of babies' hands and feet in wet clay, and create casts.
Popular for children's parties, hen parties, and general entertainment in school holidays, these cafés can get busy. So although you can normally just turn up and paint, they encourage a phone call in advance, especially if you're travelling any distance. Some techniques such as block printing require advance booking. Adults are welcome to get creative, and some places have late opening for adult-only sessions in the evenings. During school holidays there are often workshops, where staff supervise kids, and everyone's engaged in the same technique together. These might even include workshops using raw clay to make items, rather than just painting premade things.
Many places are also cafés in the normal sense, selling tea, coffee, cold drinks, cakes and so on, and occasionally more substantial fare.