Other than Cate Blanchet in The Seagull, what will be opening in the West End and institutional theatres in London this spring? Seems difficult to find scheduling past December.
If you are looking at coming in February/March, Tom Hiddleston & Haley Atwell will be starring in Jamie Lloyd's version of Shakespeare's Much Ado About Nothing. Also, The Producers will be running at the Menier Chocolate Factory through March 1.
The idea is to work and to experiment. Some things will be creatively successful, some things will succeed at the box office, and some things will only - which is the biggest only - teach you things that see the future. And they're probably as valuable as any of your successes. -Harold Prince
Like any listings site, this one is incomplete, but it does sort by month, so I often use it as part of planning a trip: https://www.westendtheatre.com/category/news/inspiration/