Let's use a nice, simple analogy and extend it from there:
Assume that an employee started work (in an uncomplicated job with a 40-hour, 5-day working week) on 1 January last year, working for the National Minimum Wage of £6.50 per hour. He took a fortnight off in October last year. So he'll have accrued his holiday entitlement during a period when his pay rate was £6.50/hr but, because the NMW rose on 1 October last year, he'll have taken his holiday when the NMW was £6.70/hr.
It's clear that his employer was obliged to pay him the same pay (£6.70/hr) when he was on holiday in October as he would have received if he was at work during those two weeks.
i.e. it's the current rate of pay when the holiday is taken that must be applied, not the rate applicable during the period when the holiday entitlement was accrued.
Therefore, for any holiday take after 1 April next year, any employee who moves from the National Minimum Wage to the National Living Wage (which, remember, isn't everyone, since those under 25 years old will still be under the NMW rules) must be paid £7.20/hr during their holiday period.
The 12-week period you refer to in your post applies to the average number of hours worked per week (including overtime), rather than to the rate of pay during that period. Further, it's not 'set in stone'. While a 2011 Supreme Court ruling [British Airways v Williams] seemed to suggest that a 12-week period would normally be reasonable, if an employee worked where there was a particularly slack period in the months immediately before their holiday (perhaps in agriculture) it might be necessary to calculate the average number of hours worked per week over a 12-month period.