The Regulations state . . .
“support group” means a group or one to one support which is organised by a business, a charitable, benevolent or philanthropic institution or a public body to provide mutual aid, therapy or any other form of support to its members or those who attend its meetings.
https://www.legislation.gov.uk/uksi/2020/1200/pdfs/uksi_20201200_en.pdf
Although the relevant regulation the goes on to provide examples, the list is non-exhaustive and can therefore include any other groups which fit within the above definition. As I see it, your group is thus likely to fall within the exemption granted by that regulation.