Since England and Wales are the only areas we visited in the UK, I can only speak to the parking in these. There is little parking. None of it is free. None. Of. It. Everywhere is paid parking unless there is a store that happens to be in its own building and has a parking lot. A grocery store or McDonalds for instance and even these aren’t vast areas. Larger shop areas may have a few hours free parking but you will have to pay for time after that. Any attraction you go to, will be paid parking. We found train stations to have the most cost effective parking for longer terms but you usually have to walk some blocks to your location when parking in these. In London, they don’t want your cars. Period. You are encouraged to leave them at home although I am not sure how you get there if trains don’t run directly to your city. You figure it out I guess. When looking for places to stay in London, hotels were very clear they did not have car parks. There are off site car parks. You just have to find them.
London is designed for you to use public transportation which is easy to master once you figure it out given there are no line closures or delays or bus detours or numerous stops on the trains and buses. All of this including walking distances must factor into your timing for getting places also which we were not used to. The underground trains arrive and depart fast and once you learn the lines and where they go they are pretty easy to navigate. Fun fact: the seat fabric colors and poles match the colors of the underground tube line. Get the TFL app or check out the TFL website for all kinds of maps including walking maps. The TFL app updates quickly with closures and delays. The Citymapper app is also a good one.
You tap in and out on the underground to pay for your ride. Be sure to use the same form of payment each time or it could consider it a different ride. (i.e. your phone or smart watch, or card). On buses, you only tap in when you get on. There is a rate cap per day and it fluctuates depending on the zone where you are traveling. Charges on our card showed up at the end of each day. There are Oyster cards you can purchase for a fee and load them with funds. It just seemed easier to us to use our phones to tap in and out.