The relevant legislation is the Employment Act 1996, but in plainer language ACAS describe that they can make deductions for the following reasons:
- the employee's contract specifically allows the deduction
- it was agreed in writing beforehand
- they overpaid the employee by mistake
- it’s required by law, for example Income Tax or a court order
- the employee missed work because you were on strike or taking industrial action
The first two provide pretty wide latitude into what they can make deductions for so long as it's in the contract/a written agreement
The employer can't make deductions that would result in your wage dropping below minimum wage except in the following circumstances:
- tax or National Insurance
- something the employee has done which their contract says they’re liable for, such as damage to a vehicle through reckless driving
- repayment of a loan or advance wages
- an overpayment made to the employee made by mistake
- buying shares, other securities or share options in the business
- accommodation provided to the employee – find out more about accommodation deductions on GOV.UK
- something the employee uses – for example union subscriptions or pension contributions
I'm not sure if it matters whether the employer is a private individual or a company
Nope - for these purposes an employer is an employer
To look at your specific examples:
but assume that the employee is not doing a very good job
No.. incompetence can get you sacked or fired - but it can't get your wages docked. At least not unless there was some performance-related-pay element to your wages already in the contract. But that would be difficult, it would have to be quantifiable. There's a reason why such structures typically have a base salary with performance-related elements paid as bonuses, because it's easier to simply not pay extra if thresholds aren't met than it is to deduct from a base wage.
snoozing on the job
Again not unless that was specified in advance - and that would be an oddly specific thing to include. Most likely they'd just get fired, in the majority of employment scenarios taking unauthorized sleeps on the job is going into Gross Negligence territory if there's a pattern.
taking personal phone calls
Taking personal calls is something that's more likely to be covered by a contract or company policy - but again it's more likely to lead to disciplinary action or sacking than wages being docked. You'd have to get into measuring how much time was lost in order to dock the appropriate amount etc.
late into work
You'd think this would be a slam dunk - you're late and therefore not meeting your contractual obligations. But in reality the same requirements as above apply - there needs to be explicit agreement in advance of the deduction in either your contract or other written consent for an employer to dock wages. It's probably more common than the other examples for such a provision to exist, but it still needs to be there.