If you want to learn about Russian culture from Russians this is an ideal starting point. They do have some links with Pushkin House too. They are friendly and helpful, not purely in a diplomatic sense, it’s their personalities too !
Programme (updated regularly, mix of free & £ events – exhibitions, concerts, education, fairs, business events)
No you won’t be kidnapped because they are Russian or any other concerns you have. They may be able to tell you if there is a tour operator offering being tailed & interrogated by the FSB – I haven’t asked them but someone I know has asked if a mild version of this exists (!)
There’s an interesting evening on brainwashing coming up: http://gbr.rs.gov.ru/en/announcements/19329
Youtube (in Russian) https://www.youtube.com/channel/UCxfs8_dijPBZQs-YihliEMA/videos
Photo gallery of centre: https://www.rusemb.org.uk/rsgallery/