Basically did the king make his presence available to peasants or regular folk? Would he give speeches to the masses? Would the average Londoner recognize him without a crown on?
It would of course depend on the specific King, but London is also a touch special in this regard. More can always be said on the matter, so if anyone knowledgeable about London-Royal relations would like to put their oar in, please go right ahead! Medieval towns are awesome.
For the meantime, OP, you may be interested in u/J-Force's post that examines Edward III and Edward the Black Prince and how they rolled with London.