>>> So I should be able to just buy and put in a card from any company?
Yes. Most providers offer SIM cards free of charge online. When you purchase on in a store there's often just a nominal charge (such as 50p or £1) if you buy a card without any credit on it but the card might come free if you purchase credit at the same time.
I'd normally suggest Asda, as their 'non-bundle' PAYG rates are among the cheapest but they're currently changing networks, so they're not providing an new SIM cards at the moment.
Many other providers either no longer offer 'non-bundle' PAYG rates or they seem to make it hard to access them. (For most people 'bundles' of call time, texts and data are by far the cheapest way of doing things but 'bundles' expire after 30 days, so they're not so good for 'emergency only' phones). Your best ('non-bundle') options though are summarised here:
https://kenstechtips.com/index.php/best-payg-sim-for-low-usage