So yes, they've broken your original contract and they're trying to make things even worse by strong-arming you into a situation that adds a ton of uncertainty. The natural answer here is sue them for lost earnings, emotional damage, etc and go back to your last employer. But there are a couple of separate issues:
Getting money out of them will be hard. We're talking a tribunal here and then chasing them across the planet to get that enforced in their jurisdiction. This isn't easy or cheap.
Your old employer is under no obligation to talk to you ever again. If your leaving hurt them or there's any animosity, you can expect a demotion and a pay cut.
So by all means talk to your old employer and ask for a firm, written offer of employment and a lawyer because you have been wronged, just don't expect these to put everything right.
Just as a quick sidebar, there are significant issues when hiring somebody full time in the UK. I say that speaking as somebody who works exclusively as a self-employed contractor for small companies here. They avoid a lot of taxes and paperwork by keeping me out of their PAYE schedule. A foreign company with no other presence here has a ton of stuff to set up.
They've probably done the sums, looked at what the worst-case outcome of being sued for lost earnings from breach of contract and have worked out that it would be cheaper to take that risk and push you toward a cheaper way of working.
They've been both stupid and nasty in a small amount of time, but given the climate of zero-hours contracts, unpaid internships, etc... They're neither the nastiest or the most unfair employer in history. There might be something to salvage here.
And if you can forgive past sins/idiocy (or your old employer won't touch you) you can make this a lot more favourable by doing one simple thing:
Get paid up front (demand an advance)
Contracts clearly mean zip for them but you can have them insure themselves against this sort of nonsense and demand as much certainty as you need in advance. If halfway through your "contract" they say they don't need you any more, that's A-Okay. You've already been paid.
So as a little not-too-silly, not-too-risky example, you could ask them to structure your payments as so:
Day 0 12 months salary
Months 1-9 Zero. Nada.
Months 10+ Normal monthly salary
If they stop paying you at any point, they breach, contract over, and you at least 3 months severance. I'm front-loading that by 12 months above because that's when companies are their most fickle.
If you need more certainty than that, ask but expect them to nibble this back. If they start getting stupid again, you can wave your offer of work back at them, the breached contract and tell them that if they try to pursue you, you have considerable UK and EU law on your side.
If buying a house is the most important thing, being employed is the most important thing here. Spend too long away from it and you'll either count as self-employed or between jobs (which can be a 6-month penalty with some lenders). Brokers can help explain your contract to banks' underwriters but you might have to put your plans on ice for a year or two.
It seems likely you might incur a loss of some description here, so if you do, please seek the opinion of a solicitor. I'm not a lawyer and your chances of pursuing crappy contracts internationally might be much better/cheaper than I'm saying.