Small groups in modern Christianity had their origin in Wesley's ministry efforts, since then they have probably drifted in and out of popularity and use. We are currently in a popular period for them.
At almost all churches that I've been part of I've also been involved in a small group (including in Eden Baptist Church whose then minister left his wife to take off with his 'boyfriend'!). I think they are an important part of church life, even more so, in some respects, than the formal 'service' (meeting in NT terms) that we enjoy.
Groups have ranged from the dictatorial and almost cultish, to the near laissez faire, and all shades between.
At Christ Church St Lawrence I was invited by one of the younger men, RH, whose circle I'd come into to join the small group hosted by the curate in his flat adjoining the church building. RH and his wife M hosted an open lunch each Sunday which was attended by about 20 to 30 people. It was a simple meal: something like lasagna, bread, salad and a glass or two of wine. People drifted home after an hour or so, with the long stayers hanging on until mid afternoon. All very pleasant with the opportunity to talk to people one might not otherwise meet.
When this lunch was not on, we drifted along to the Graphic Arts Club (where my father had been a member, I recalled with some pleasure) for our lunch.
I felt honoured to be invited to the Bible Study, given by Fr Reg and impressed that R stressed that we met for evening Holy Communion at 6, followed by a cheap meal locally, then the study. It was a whole package, and not just a chat session.
The study was very different from my evangelical experience, but a very good 'different', given the different view of the church had there and the air given by the preceding service. There was also something I couldn't put my finger on, but there was a certain specialness in having a 'priest' involved. In Reg, a very engaging priest at that.