subject to the disclaimer that i'm not a lawyer and it's a while since i have been a union rep...
i think where they are based is irrelevant - they are (unless this was clearly agreed in advance) employing you in the UK, and therefore UK employment law would apply (the whole 'work from home' thing is relatively new, i'm not sure how it works if an employee voluntarily goes for a job with a non UK company and works from home in the UK.
just because something is in a contract doesn't necessarily make it legal or enforceable - a contract can not over-ride employment law.
you have few protections against 'unfair dismissal' until you have 2 years' service in. (although dismissal because of discrimination on one of the grounds in the equalities act, and i think for raising genuine health + safety concerns, or simply for being a trade union member, apply from day one.)
one week's notice is legal minimum after you've been employed for a month. more on this at ACAS website
here.
from
same source there does not seem to be anything in law about notice periods to resign, or anything about unbalanced notice periods. there might be an argument that this is an 'unreasonable contract' but not sure i'd want to offer any thoughts on that.
i understand there is precedent of companies suing for damages if an employee fails to give contractual notice to resign, but think case law has held that they have to prove they have incurred losses (e.g. paying high day rates to an interim worker, or losing business or something.)
i think they would be on thin ice if they witheld wages and accrued holiday pay you have already earned if you quit, although you would probably have to take them to court / tribunal and argue about it.
without knowing what you do, and what they do, i don't know to what extent 'the same industry' would be an issue. you say you're a PAYE manager - so would that be classed as 'your industry' or would whatever line of business they are in be 'the same industry'? my gut feeling is the latter. would you be able to get another job as a PAYE manager or similar for a company in a different industry? (or are you in a particularly specialised niche?) it's not something i know a lot about, but would have thought it's a specialist role that can be done in most industries, so not sure this is much of an issue. but i may have misunderstood something.
and if you went back freelancing, even short term, would they even know?
ACAS say "this area of the law can be complex" when it comes to restrictive covenants - something saying you can't go and work for a competitor, or where there's a conflict of interests (e.g. going and working for a supplier / customer) is not unknown. but this seems dubious for someone who (if i've understood right) isn't really doing anything in the technical / creative side of their business.
i'm not sure quite where you stand if you're already a couple of months in to the job and only now see the contract, and how much of it they could try, let alone succeed in, enforcing, if you tell them you're not accepting it.
i'm inclined to think you want advice from someone more informed than me.
are you in a union? that would be the obvious, failing that, ACAS do have
an advice line that individuals can call, although i don't know how far they would be able to go with the specifics here.
