How do you prove you can't afford it to the zoo? You can't.
How do you define "can't afford it"? Cash in the bank but other priorities? No cash in the bank because it's all tied up in long-term savings accounts? High wage earners who have large mortgages and private school fees, leaving little for days out? How about someone on a low wage. What if they have a high wage partner? What if they don't have a job? But they're supported by rich parents who pay for their house and credit card?
What is very easy to do, however, is prove you claim UC, which almost certainly means you're on very low income and genuinely can't afford it.