I have a friend who was almost the buyer of a house in the UK in a very similar situation. Fundamentally, it relied on the seller buying counterfeit identity documents (passport and driving licence) off the internet. That way, in theory, the identity checks were all conducted.
There was the suggestion that the seller's solicitor was in on it, but no firm evidence. The seller has been arrested at least.
It's a shame that the systems that are really important, like passports, id cards, property registers etc. are all still so far behind in basic security. They could easily require certain info up-front on the title like mobile, photo etc. and then if you need to update it, you have to do it via a solicitor or equivalent, it's not like most people change their photo or mobile number every week.
But the phone number system isn't perfectly secure. A fraudster could transfer your account or even have physical access to the phone line. And it still relies on a solicitor to authenticate changes which could then be fraudulent.
The advantage of the current system system is that it is fairly explicit and public. It can be checked without any secret codes or processes using the information on the title itself.
There was the suggestion that the seller's solicitor was in on it, but no firm evidence. The seller has been arrested at least.