Major UK mobile operators are Vodafone, O2, EE, Three. All other operators (Lebara, Tesco...) do not have their own networks.
Free SIM cards of mobile operators:
- Vodafone. You can get it via charities: Red Cross, Barnardos (if you have children), Citizen advice bureau.
- Three. You can get it in the Three mobile operator shops.
- Lebara. Available in retail stores.
Today major networks allow free calls to Ukraine and free roaming in the UK: https://www.techradar.com/uk/news/uk-mobile-operators-offer-free-calls-to-ukraine-waive-roaming-charges
You can buy a SIM card at the (air)port of arrival. It will cost about £10 per month for unlimited calls and messages, as well as several GB of data. SIM without a contract is called Pay as You Go. The number can then be transferred to another operator. If you want to join a contract, you need to know that if you want to terminate it early, you will still have to pay until the end of the minimum term of your contract.
More useful information here: https://bit.ly/ua-uk-faq.