I know I’m gonna get some stick for this, but have always found the LLC people OK to deal with (contact them by e-mail is best) they seem quite pragmatic and understand that lorries are essential to London (I’m in construction haulage) make sure your vehicle is on their database & delivery dockets prove your destination,Sorry to say a lot of problems are down to ineffectual TM’s, planners or traffic clerks, (just blame the driver when the ■■■ hits the impeller he can pay the FPN) 
I have been the exact same way, and thought the exact same as you, and this was a good few months ago.
Was going to spin in round at the roundabout, but the exit I wanted was not signposted as not for 7.5 tonne and above, so I carried on regardless.
I have heard nothing from my Transport Office regarding any penalties, so I assume that what I did was alright.
I would fight it if anything did come back, as the signs are not consistent.
I have made one complaint because a lot of the signs show a 16.5tonne weight limit and I have been assured by London Councils that it is 18tonne and the respective boroughs that have the signs have not updated their signage■■?
