Influence Sources

Stolen Correspondence
If you still have access to the Court, 'Write a letter' & 'Attend a dance' under "Attend to matters of romance" grant 18 per action. Play the "The Big One" storylet in the Flit. Rob the Chambers of the Duchess, then choose Rob the Study: that will give you 300 Stolen Correspondence! You can also grind in Spite; 'Ambush a few couriers for old times' sake' costs 2 actions but grants 40 Stolen Correspondence on regular success, or 20 and a Love Story on a rare success.

Intriguing Gossip
Convert from Stolen correspondence or get them on the 'A meeting with his peers' choice from 'Visit your acquaintance, the Wry Functionary'. Another option is Acquaintance: Sardonic Music-Hall Singer cards. sells for 20 pence

Compromising Document
http://fallenlondon.wikia.com/wiki/Something_troublesome is very good source, as even 'fishing with fisher kings' in Flit can net 1~8 of them. If you have access to the Foreign Office, the storylets there will give Compromising Documents. Or convert from Tale of Terrors!. sells for 50 pence

Secluded Address
'Advertise a spot of hunting' while Fighting the Big Rat provides 3, along with 3CP of Running Battle and some Scandal. For less frequent option, use the Yacht card at Zee, or poke your plant in 'Your plant is singing' card.

Stolen Kiss
Convert from Compromising Document, Grind these at Polythreme Streets, donating 500 Glims to 'The Soft-Hearted Widow' card gives you 2.

Favours in High Places
Convert from Stolen Kiss or see the components page. component - sells for 12 Echoes, 50 pence