No, this is not possible. PayPal only supports:
transfers between two PayPal accounts, and
transfers between a PayPal account and its associated bank accounts or cards.
This makes PayPal unsuitable as a general payment method or as a general-purpose bank account.
To transfer money to a recipient who doesn't want to open a PayPal account, you will need to ...
Well a friend offered to buy that ticket for me and I'll transfer the money back to him. But I also got a reply from ANZ bank.
It appears the answer is generally "NO", but also "maybe yes if you ask each time you need to do so".
Here's the main parts of their reply:
Regretfully your new request is not possible because it defeats the
purpose of ...
Cash is an option. It's less common than in Europe, but 40 £20 notes are not that difficult to count or keep secure. If you are worried about security, you also need to worry about the "purchaser" just running off with the laptop without even pretending to pay.
It's almost entirely safe to give out your sort code and account number. You already do this if you ever write a cheque, for example.
There is a small risk that someone could set up a fraudulent direct debit in your name. But those can only be to organisations that accept direct debits so there's not much motive to do it, and you'd be able to reverse it as ...