Don't recall if it was ever explicitly stated where you emerged from Below in CoP (and a quick check around page 81 of the thread confirm that it wasn't - unless it's buried in the OoC somewhere
) - assume somewhere mid way between Nightside and Earl's Court?!?
The LCZ is most of the south of London so they can't possibly guard every entrance - there will certainly be checkpoints at the river crossings and on the tube stations leading in/out, and there are 3 barracks with approx. 3000 soldiers according to the old London sourcebook. It should be easy enough to get past the guards, particularly if you are concealing your weapons already. They are more worried about armed mobs than individuals coming and going.
Robyn has contacts with the Mechanica (Steampunks natch) in Southwark Cathedral...they could provide you some cover to get into the LCZ and then Below as they operate in both places.