I'm just wondering whether there is some confusion in some of the answers to the original question, which is whether the UK customer of a Belgian service provider has to pay VAT on the Belgian-source invoice if the UK customer cannot produce an EU VAT ID (the rules on these VAT IDs and their composition differ from country to country, by the way).
The answer is: Yes.
No VAT ID = UK Customer pays VAT in exactly the same way that the UK customer has to pay VAT on invoices issued by UK businesses.
Thank you all for your contribution.
I think RobinB's answer is the perfect summary. As a side note I think it's an understatement to say that 'some government rules could be clearer'.
I have put the exact same question, in writing, before HMRC. If and when I get an answer, I will add it to this post as closure.