In a London Control area sector it will make little difference requesting a reroute as the computer is good enough to provide all the controllers your details to ensure safe passage. If you are significantly off course then there is the possibility that London have already rerouted you themselves to get the next sector/centre the correct details too, however this isn't an official reroute as such and pilots are rarely informed.
Your profile doesn't say where you are based +TSRA, however if you can ever get to Swanwick, Southampton then the TRUCE program (about to be renamed as ABES SIM), which is the controller annual check, always welcomes pilots to attend. This year there is a piece about severe weather avoiding......... You can find details and who to contact here in the
Rumours & News forum.
Edited to insert the link to the TRUCE thread in Rumours & News.