From the BAEC terms and conditions:
14.5. If a Member has not earned or redeemed Avios points or purchased or transferred Avios points in accordance with the Conditions of Use for 36 consecutive months, all Avios points that have accrued to that date will expire.
...
18.1.17. The Avios points balance of individual Household Account Members shall expire in accordance with Clause 14.4 if the individual Household Account Member has not earned or redeemed Avios points or purchased or transferred Avios points in accordance with the Conditions of Use for 36 consecutive months. Notwithstanding Clause 3.12.1, in such circumstances, the membership of the individual Household Account Member and the Household Account shall continue in effect.
From the household account thread:
If a Blue or Bronze member has had no activity in 36 consecutive months but they are part of an HHA which has a Gold or Silver member their Avios will be protected as long as there is an active Gold or Silver in the HHA. Other than that, make sure you keep an eye on this and ensure all accounts have some activity occasionally – of course, the easiest way to do that is a redemption due to the formula above.
You are responsible for tracking your avios activity.
See also these threads:
https://www.flyertalk.com/forum/brit...os-expiry.html
https://www.flyertalk.com/forum/brit...-accounts.html
https://www.flyertalk.com/forum/brit...-expire-2.html