Mike, It is fairly simple.
PAYE periods are defined by their end-date. So weeks ending between 6th-12 April are week 1, between 13th-19th April week 2, and so on.
Week ending 5th April is week 53 and week ending 4th April is Week 52, except in a leap year where week ending 4th April is week 53 too.
Month that ends on any day from 6th April to 5th May is month 1.
4 weekly period that ends on any day from 6th April to 2nd May is week 4.