Multimodal routing in the UK - what sites/tools?

When routing for non-driving travel around the UK (though a Europe-wide answer would be very interesting), is there a tool that allows a sensible mix of public transport and walking (possibly with cycling, especially bike-share schemes, possibly with ridesharing)?

This is something I've been thinking about recently*, and we've just had a London-specific question, so here's a more general version. Such a tool would also have been handy when planning the route in this answer.

Even with "fewer transfers" set in Google maps, it seems to avoid even quite short walks in favour of changing buses/trains. When the buses are infrequent this can take a lot longer than walk+bus. To route manually requires some local knowledge/guesswork about which bus stops or stations to walk to; while possible on the desktop the mobile interface isn't much help. Traveline is worse, finding solutions using 3 buses where Google uses 2, and not even saving any walking.

One feature that might help with routing efficiently but would certainly allow planning a more interesting route would be to allow a "via" option when using public transport, as you usually can with walking/cycling/driving directions.

* _{I'd normally cycle a lot (even sometimes between cities) and drive occasionally; an injury means neither is currently an option but I can walk quickly. Planning efficient routes is proving rather tedious even within/between cities I know.}