The Council of BSHM is elected at the AGM in October to serve for the whole of the following calendar year. The Council for 2023 is as follows:
- President: Sarah Hart
- Vice President: Chris Hollings
- Secretary: Fenny Smith
- Treasurer: Simon Gardiner
- Membership and new members Secretary: Dorothy Leddy
- Meetings Co-ordinator: Brigitte Stenhouse
- Education Officer: Ciarán Mac an Bhaird
- Communications officer: Dorothy Leddy
- Web Admin: Troy Astarte
- Elected (ordinary) Council Members: Máté Szabó, Deborah Kent.
- Co-opted Council Members: June Barrow-Green (JMC) .
The Journal Editor for 2023 is Isobel Falconer, who is not a member of Council.