I used to have afternoon tea with friends quite often - if only because that was the time they picked up children from school / nursery and brought them home. We would have sandwiches, biscuits, cake and lots of cups of tea! I think part of the reason is that, certainly our group, ate supper much later, 8-9pm, so something to keep you going until then was a good plan! Plus it was a good excuse to get together for a gossip, and open a bottle of wine (after 5pm of course...) if required (it normally was required!)
Near my parents, the retirees all seem to go out for afternoon tea - the local garden centre is packed out between 3 and 5 each afternoon with the blue rinse brigade! And quite a few of the restaurants and upscale pubs have also cashed in on the market, during their slow period between lunch and after work drinks crowd, by offering things like fancy coffees (and the usual tea, but Brits are heathens who drink milky coffee in the afternoon!) and teacakes, scones etc.