there's actually a lot of places that aren't on the bike park map because they aren't 'official bike bays'. For example, round my office the map shows no bike bays but there's enough unofficial spaces for at least 50 bikes.
Near Ian's location, there are actually a few spaces at the hospital opposite the London Dungeon. I didn't mention it before because the security guards will let you get away with it once or twice but not on a regular basis.
My recommendation would be to get the train the first 2-3 times but get there early so you can have a walk around the area and check where the locals park (easily spotted if you see the same bikes in the same locations). Make sure that you check there are still spaces free around the time that you would normally want to get there.