Fortunately there's another identifier - the Unique Property Reference Number (UPRN) - that exists to, well, uniquely identify every property in the UK.
Currently it's proprietary but from July 2020 it will be available for use under the Open Government License.[0]
[0] https://mhclgdigital.blog.gov.uk/2020/04/02/unique-property-...
A previous discussion on this, in 2013, tried to give some examples. None of them seem to break the rule, since "Pleasant Cottage" and so on are building names. If there's a counterexample, Wikipedia should be updated.
My house has a number, but for some reason it's listed under the "name" of my house - no end of confusion.
I think the other address was supposed to have an East before the street name, but when they left that off I got (some of?) their mail.
Should have figured out my +4 and tried that.