Pay As You Go SIM Card
There is one exception. EE offer a Pay As You Go SIM. It is not advertised on the website and I had to ask in an EE shop. The minimum initial payment is £10. The SIM needs to be used at least once every three months to keep the credit.
The charge rates are a rip-off: 20p per text and 40p per minute for calls, but if it is hardly ever used it is a lot cheaper than paying every month for something you don't need.