What makes this vibe
Britain is one of the best countries in the world for being indoors, which sounds like faint praise but isn't. The gallery infrastructure, the market culture, the café density, the Victorian covered markets and conservatories, these were built for a climate where being outside is unreliable. They are very good at what they do.
The Barbican Conservatory is an extraordinary place in its own right; it is extraordinary specifically because it puts you in a tropical garden when you walk in from February concrete outside. The Tate Modern's Turbine Hall is a different kind of experience on a wet Tuesday than on a sunny Saturday, quieter, more immersive, less crowd-managed. Borough Market's covered sections keep most of the experience rain-accessible even on wet days.
Planning for rain
Build indoor-outdoor flexibility into any UK plan. The morning market works if it's dry; the covered gallery is the contingency. Know in advance which of your planned stops work in rain and which don't, so the decision requires no thinking when the forecast proves accurate.
The best rainy day experiences are ones that would be good regardless, the rain just tips the balance from "we should go outside" to "we're very happy where we are."
The silver lining
Rainy days in the UK filter the crowds. The free gallery that had a 20-minute wait on the sunny Saturday morning has space to breathe on a wet Tuesday. The market that's overwhelming in full summer is navigable in October drizzle. The trail that requires early starts to avoid other walkers is empty in a storm. Not all rain is bad news.
