The reason for squawking 0013 without talking to anyone, though listening out on the appropriate frequency is stated in AIC Yellow 228. See the extract below
"A pilot flying around the peripheries of London Luton and London Stansted Controlled Airspace, as depicted on the attached map, that does NOT require any air traffic service may elect to squawk SSR code 0013 with Mode C selected if available, whilst monitoring either Luton Radar on 129.550 Mhz or Essex Radar on 120.625 Mhz."
Departing from White Waltham (EGLM) towards Bovingdon (BNN) means that the start of the flight is within the westerly area of coverage of Farnborough LARS, therefore the first call should be on 125.250 if a FIS is required.