Does it matter whether employer is company or individual?
Must certain amount of notice be given?
Yes - the notice period maybe specified in the contract but even if it isn't there are statutory notice periods that apply depending on length of employment etc.
So if the following criteria are met
- they are legally classed as an employee
- they have worked for the employer for at least a month
Then certain minimums apply:
If they have worked for the employer for:
- 1 month to 2 years – statutory notice is 1 week
- 2 to 12 years – statutory notice is 1 week for each full year they have worked
- 12 years or more – statutory notice is 12 weeks
A notice period in the contract (i.e. "contractual notice") can exceed the statutory minimums but it can't reduce them.
What other requirements are there that must be followed?
This is pretty broad and I don't really want to reproduce everything here but the ACAS page on dismissals covers the basics.
Can notice be dispensed if the task is of an urgent nature and employee must be replaced as a matter of urgency?
Dismissal without notice is possible in cases of Gross Misconduct but that is about what the employee has done - nothing to do with the urgency of replacing them.
However, if both parties agree a notice period can end early:
The employee can ask if they can leave before their notice period ends.
They should get agreement from their employer in writing. If the employee does not get agreement to leave early they could be in breach of contract.
If the employee leaves early, the employer only has to pay them for the time that they’ve worked.
If an employer wants them gone immediately they can do that if it's either in the contract but they still have to pay them for the notice period. They can also offer payment in lieu of notice if it's not in the contract but it's then up to the employee if they agree.