Income tax and NI for secondary employment

Hi. Complete novice here. I know very little about tax and NI, so please forgive ignorance. I have been working for the same employer (in the public sector) for several years. Obviously all tax and NI deducted at source. Then around 18 months ago I started doing a bit of additional work in my spare time for a private company (all with the permission of my primary employer). The combined income from primary and secondary employment took me over the 40% tax threshold. Income tax on that secondary income was initially done through self-assessment. My work for the private company was intended to be only temporary. However, a couple of weeks ago the company offered me a long-term contract and wants to put me on the payroll for tax purposes. I am perfectly happy with that arrangement. However, my question is: Will the private company be aware that the income they pay me takes my total income (including my primary employment) over the 40% threshold, and will they tax me at that higher rate accordingly? Or will they just tax me at the basic 20% rate and expect me to make up the difference through self-assessment? Also - and again forgive my ignorance - what about NI contribuitions? For the 18 months I was doing self-assesment for the secondary income, I did not pay NI contributions on that income. Will the private company deduct NI contributions once I am on their payroll? And what did I lose from not having paid NI contributions on the secondary income for the 18 months I was doing self-assessment? Many thanks.

Hi,

The company will initially tax you at basic rate until they receive a revised tax code from HMRC. They will not be told of your other income.

The National Insurance will be covered by your main source of employment.

Thank you.