What is the word for "taxpayer identification number" in England.

Employer ID number?
Federal Tax Identification Number?
Tax ID?

What about employees? Do they have this number?

Thanks in advance.
Thank you, you've just reminded me that I have to complete and return my tax forms for this year.

In the UK it is your National Insurance Number that is used to identify an individual for both tax and social security purposes. The Inland Revenue(Tax Office) may give you a tax reference number on any communications but the N.I. number is more important.

Employers will have this number if they are employing you legally because they are legally bound to pay part of your National Insurance contributions and deduct income tax from your salary.

Employees are normally given a form, I think it's a P62, when they leave an employer and they are legally bound to pass this onto their next employer whenever they change jobs. This is a statement of how much tax they have paid to date in the current financial year. This will have their N.I. number on it.
Thank you very much for your explanation.