Similar to my situation in Helsinki, as soon as I moved to my new apartment, I needed some way to get to work.
As happenstance would have it, my temporary apartment ended up being in Paddington instead of one of the neighborhoods I was checking out (which was the original plan), so I was walking to work the first month of the time I was here in London. What that meant in reality? No extra transportation costs on a daily basis.
This actually saved me a boatload. Monthly transit passes in London are quite expensive. I'll give you an example. From the zone that my new apartment is in (which is zone 3) to the zone that my work is in (which is zone 1), a monthly unlimited transit pass is approximately 120pounds. Yeah, that's right, 120pounds.
So let's just say for the sake of awesome savings that I saved myself from having to pay 120pounds for that first month. And you can do the math on how much my transit fees are generally going to cost for a year.
But that's sort of getting ahead of myself. Because I didn't need to buy that pass for the first month I was here, I just used my Oyster Card (an electronic card, very similar to my futuristic bus pass in Helsinki) to get around the tube and buses whenever I needed to go somewhere (i.e. sightseeing with my parents on the weekends or out with friends on various other days). Other than that, it was just walking.
Anyhoo, when I got to my new apartment, it was time to buy that annual pass. When you buy an annual pass versus a monthly pass, they do give you some savings. Again this depends on which zones you're buying (you buy zones that you're interested in traveling in; unfortunately there's no all-encompassing awesomeness like in Finland unless you want to buy zones 1-6 which probably costs a fortune) and then they give you a discount accordingly, like 15-20pounds a month savings. This is pretty good because the monthly pass is already saving you about 50%, assuming you are going up to the max of 10pounds a day (they won't charge you more than that per day if you buy an unlimited day pass...but anyway, I'll not get into that because it gets very confusing).
So, time to get my annual pass.
There were two options I could get: get an annual pass Oyster Card or get an annual pass transit card. The Oyster Card tends to be associated most with the underground though it can be used for all transportation types and is pretty convenient because it's a magnetic card. The transit pass covers tube, buses, and overground trains and comes with an ID card. Both are registerable so if they get lost or stolen you can gave them replaced.
At the end of the day I decided to go with the transit card. I wanted to have an ID card and I'd be taking the overground train everyday. Plus I found out that it allows me to get additional benefits like a 30% discount on tickets for up to 3 people if I'm traveling with them. Or discounts for myself on areas outside of my zones (so trips to the airports, for example). I can also get weird 2 for 1 admissions and discounts to various attractions around the city. So, pretty much blasted the Oyster Card out of the water as far as savings are concerned.
The only serious drawback about it: it's a paper card with a magnetic strip. So everytime I come across a station entry with turnstiles, I need to slip my card into the machine, like a day pass (versus an Oyster Card, which I can swipe on the machine).
Unfortunately no pass that I could buy easily would get me to or from any of the airports for free so that's a benefit that I've given up from Finland (it was nice being able to take public transportation as part of my pass), but oh well. London, you're certainly proving much more expensive, in all ways.
But at least I can now ride unlimited on all tubes, buses, and overground trains within zones 1-3. It's nice not having to worry about that. And I just got the money back from having turned in my futuristic bus pass back in Helsinki (I still had time left on it so I turned it back in). So that's something. London, you are going to be explored. :D