No, they can't force you to work per se, but you could (in principle) be sued for breach of contract if you don't serve your notice period.
Most employers are fairly pragmatic in the UK. If the employee requests a shorter notice period at resignation time, and they're not actually on the critical path for something, most employers will agree. If the employee doesn't request a shorter notice period, many companies will stipulate that all unused holiday allowance must be taken at the end of the notice period - so the pay period is exactly the notice period from resignation, but the employee finishes early.
> Think of a non-compete as a 6-12 months notice period when you don't have to work
That's fine if you're on paid gardening leave. If you're not being paid, they have no right to dictate whether, or for who, you can work.
> (and can actually work for a whole bunch of different jobs, just not for the competitors).
Typically in the UK, the provisions of gardening leave explicitly state that you cannot undertake any paid work. You can study, you can do DIY, you can do garden work (hence the name), even do voluntary work, but you can't take on any other paid work.
> Consider a sales manager going to a competitor with the knowledge of prices for the top 10 customers.
Typically, if the employee took commercially sensitive customer data (and that includes names, position, phone, email address), then they could be sued for breach of contract. It doesn't matter if they copied the data via USB stick, printed it out or memorised it - they're still breaking the non-disclosure agreements they'd have signed.
I should probably clarify that there are non-compete agreements in the UK, but typically they're not enforceable and the real reason they're there is to scare the employee. They're not part of employment law, and so it would be deemed to be a normal contract that would be tested in court based on reasonableness, and in general an employee's right to work would override any restriction in a previous contract. There's actually consideration going on right now that recognises that non-competes exist and to restrict the scope of them. To quote the document [1] that describes the status quo:
> There is no provision in the UK employment statutory framework for non-compete clauses, including in Northern Ireland where employment law is devolved. As such there is no statutory definition. However, non-compete clauses are subject to the common law principle of “restraint of trade”. The principle provides that a worker should be free to follow his trade and use his skills without undue interference, thereby rendering a contractual term (such as a non-compete clause) purporting to restrict that worker's freedom to work for others or carry out his trade or business void unless it is: (a) designed to protect legitimate business interests; and (b) no wider than reasonably necessary.
> Consequently, even where non-compete clauses are found in employment contracts, they may not necessarily be enforceable, unless a court considers that the non-compete clause is to protect a “legitimate business interest” and is no wider than reasonably necessary.
> Simply proving that the employer will suffer from “more competition” is not counted as a legitimate business interest. In broad terms, the courts have recognised that a legitimate business interest may include protecting trade connections (with customers, clients or suppliers) and, more generally, goodwill; trade secrets and other confidential information; and maintaining stability of the workforce.
[1] https://assets.publishing.service.gov.uk/media/5a7f68b440f0b...