Is income tax worked out monthly?

With my overtime I have stepped into the 40% bracket for this month (over £3116). Do they tax me on a yearly average or just monthly?

Income tax is calculated on a yearly basis. But when you are employed your annual income is estimated each month based on what you have earned so far that year. Then your estimated annual tax liability is worked out. Taking into account the tax you have already paid they divide the amount estimated by the number of months left in the year and that is your tax deduction for that month.

If your pay goes up and down then your tax will change as well. If it looks like your annual earnings will be over the 40% threshold then you will be deducted some 40% tax. But you will get this back in the following months if your pay goes back down again. Certainly by the end of the tax year (April 5th) you will end up paying the right amount of tax.

Income tax is calculated each payday, usually on a cumulative basis. Whether you are talking about tax allowances or rate bands both are proportioned out throughout the year.
You say you are paid monthly. Income tax month 6 is between 6th September and 5th October, so I guess you may have been paid in income tax month 7 if payday after that date. It depends on the amount of your next pay. If it is much less, you will drop back into only the 20% rate band, and get either a refund or a smaller tax deduction. PAYE automatically adjusts according to latest pay in the year.
Although http://www.listentotaxman.com is a good site, it doesn't give you an in-year calculation. You can do it roughly. If your code 647L, personal tax free allowance is approximately £540 a month. So £540 x income tax month number. Take away from gross pay. If monthly average left more than £3116.66, you will be paying 40% on excess. 20% tax is due on first £3116.66 a month.

They tax you in bands - if you step over the 40% threshold, you aren't taxed 40% for everything you earn, only the £3116 is taxed at 40%.

You have a personal allowance of £6,475, which is not taxed.

The next £37,400 is taxed at 20%, and anything over that is taxed at 40%.

So, if you earned £47,000 over an entire year, you'd pay about £13,000 in tax and NI.

If you want to see your taxes for the month, go to the site below and enter the details.

yearly only for sure.