What about something like Windy.com? You can use their ‘embed’ feature along with our Custom Tiles to get neat animated and interactive maps.
It looks like you could also embed the Met Office maps, but the navigation bars on them are pretty big, so you would need a large tile just to be able to display the content. For example, even in a 3x3 tile (standard size), you can see how the navigation kind of takes over:
PS. Some people prefer to use the Refreshable iFrame Custom Tile I put together along with their weather map URLs as it can periodically refresh things in case the source site doesn’t automatically refresh (or times out after a period of time).