Julian, I've never heard of an a/c asking to slow due to weather avoidance, just for turbulence or if weather at the destination has caused a backlog in the holds.
As I've said on weather avoidance threads before, always ask first. The London sectors are so tightly packed together now that unknown deviations can cause all kinds of trouble. The mass avoidance we had earlier in the year (discussed on another thread in here) proves the point exactly. We do flow our sectors when lots of weather is known so hopefully the frequencies shouldn't be too loaded, and taking a turn toward a rather large French danger area is the last thing I really want to try and co-ordinate, not having fighter control training and missing 3 Mirages going full tilt aint that easy.