The allowance is calculated on an annual basis overall.
But each month is for PAYE purposes treated pro rata,so you could land up paying 40% in a very good month and then get it back the next/following month
The amount has to be over £3740 before you pay higher rate tax - and then only on the excess, not on everything. Your (rough) figure of £3000 omits to take into account your personal allowance
And also it's cumulative - you'll get it back the following month if your annual allowance