The Council of BSHM is elected at the AGM in October to serve for the whole of the following calendar year. The Council for 2019 is as follows:
- President: Mark McCartney
- Secretary: Fenny Smith
- Treasurer: Klaas Sijbrandij
- Membership Secretary: Ken Lord
- Meetings Co-ordinator: Isobel Falconer
- Education Officer: Snezana Lawrence
- Communications & New Members: Dorothy Leddy
- Webmaster: Troy Astarte
- Elected (ordinary) Council Members: Christopher Hollings, Robin Wilson. Co-opted Council Members: June Barrow-Green.
The Journal Editor for 2019 is Benjamin Wardaugh, who is not a member of Council.