The new NMW comes into effect from the start of the first pay period beginning on, or after, 1st October. So, for example, someone who works Monday to Friday and gets paid on a 4-weekly cycle, with the current cycle ending on Friday 24 October, won't be entitled to the new NMW until Monday 27 October.
"When calculating your pay rate you use the National Minimum Wage rate in force at the start of the reference period. So, for example, if you are monthly paid and your pay period starts on 10 September and runs until 10 October, you will be entitled to the National Minimum Wage rate in force on 10 September for the whole period, even if the National Minimum Wage rate changes on 1 October."