Calculation of income tax after a job change

[FuzzyLogic]

Until August this year I was working for company 'A'. I then moved to company 'B'. In the process of moving to company B, I took a good pay rise, however I am not sure my PAYE tax deduction is now correct.

Please can someone explain the correct method for manually working out what I should be paying. Most of the online calculators I have found assume a flat income for a year.

Thanks.