Hi,
I'm in the UK and live in on the outskirts of London, regularly using public transport to get around the city. Hopefully the information below will be helpful. I rarely get a chance to contribute to the forums as our seats / vehicles / regulations are quite different, so hopefully the information below will be some return for the helpful advice I have been provided recently.
The London Underground (Tube) is excellent but regretably not that reliable. The system is well over 140 years old and at times it shows. Be aware that major engineering work takes place on weekends on most lines (including the new overground network) and this frequently results in planned closures. You can find out about planned closures by visiting
www.tfl.gov.uk.
This will show both planned closures and live delays/problems. If you have an iPhone or similar I suggest bookmarking the page so you can check whenever you deem it necessary.
Information regarding these closures can also be found at all stations on a large whiteboard near the ticket barriers. The phrase "Planned Engineering Works" covers a multitude of things ranging from complete line closures to reduced escalator services (which maybe important if you have a pushchair).
Secondly, the stations vary greatly with regard to ease of use. Many of the newly refurbished stations (Kings Cross St. Pancras for example) have very wide tunnels, good lift services and modern systems which make life very easy (although at King's Cross St. Pancras you might feel like you've walked halfway across London when changing lines - it is huge!). Nonetheless older stations can be a real hassle to navigate fluently; not only are some of the walkways and tunnels fairly small but often escaltors can breakdown and you are forced to use the stairs.
For this reason I suggest studying the map in detail. Although it is a wonderful piece of visual communication and design it's one criticism is that it does not paint an accurate geographical representation of the city and as such some tourists can easily find themselves paying for a tube journey when it is easier and quicker to walk.
Examples of such include Leicester Square and Covent Garden which are only 250 yards apart at street level (which in my opinion is most definiately not worth paying the Tube fare for as it is quicker to walk) and Bank and Monument which are actually the same station (technically this is indicated on the map but can be easily overseen).
Forgive me if I'm rambling but my point is that a comparison between the street map and the Tube map is well worth doing as it can save you time and a significant amount of money.
I highly recommend buying an Oyster Card. They are easy to use, easy to top up and most importantly will always charge you the lowest fare as well as being universal to all of modes of transport run by TfL. And as I'm sure you have no doubt seen, the Tube is VERY expensive when buying regular tickets.
Also, I don't recommend bothering with Travelcards. The rules were changed in December of last year so that you cannot spend more on an Oyster Card in one day than the cost of the equivlient travelcard. Therefore there is no gain in purchasing a Travelcard. Does that make sense?!
Finally, be aware that due to the age of Tube, the journey is often hot and noisy. Always have a bottle of water with you because no trains or stations are air conditioned.
Having said all the above, I love the Tube and it provides a fantastic service for the majority of the time. I would recommend it to anyone over buses for its simplicity and efficiency when it is running smoothly.
Buses are much the same. The old joke of "It's like a London bus - none for a hour and then two turn up at once" is unfortunately quite true. They have made huge improvements over the last few years and generally the drivers will help you out if one asks nicely (some can be quite short in their response but I assure you it's not purposefully inpolite - driving in London can be stressful!)
Black Cabs are expensive but generally very good as previous posters have stated. Don't forget also there are some areas of London which have trams which are also very efficient.
With regard to car seats I can't really help too much but the law here is that all children younger than 12 or less than 135cm (53") must travel in some form of car seat, be it rear-facing, a forward-facing harnessed seat or a booster seat. If you need more information on this visit
http://www.direct.gov.uk/en/Parents/Yourchildshealthandsafety/Roadandtravelsafety/DG_10037077.
I hope this is not too much information and that it is helpful. If you need anymore information on getting around London please let me know and I'll do my best to help out. My apologies if I have mentioned that of which you are already aware!
I hope you enjoy travelling around London, it really is an incredible city. The UK might be small but there is so much we to have offer!
Thanks,
Gary.