You cannot work for free under Minimum Wage legislation.
You got a reference for that? Minimum wage legislation allows pay to be aggregated over a period, so unless the unpaid section takes that total pay below national minimum wage it does not apply.
So in the case of 1 week in a 28 day pay period, unless the remaining 3 weeks came out below min wage for 4 weeks, its irrelevent. I'd be suprised if any BA staff were affected.