Not a lot of similar situations, but there are some, such as taxes (particularly VAT, and to some extent self-employed Income Tax).How many other situations are there where a company can say "you owe us £x - we have no proof of that, we're just guessing, but you have to pay"?
However, I imagine that a court would probably sympathise with the situation, since the individuals (or companies) can be said to have "brought it on themselves". Before an estimated bill' was issued, they would have been told that "if you provide meter readings (or VAT/Tax Returns/whatever),then we will bill you for exactly what you owe us, but if you don't provide that information we will have no choice but to issue an estimated bill".
The estimated bills are, of course, not 'blind guesses' but are usually true estimates based on historical data, and will rarely be grossly incorrect.