Transportation in London - taxi or tube?

In your situation I would not recommend the tube. There is a lot of walking in the underground stations including steep stairs. You will also need to transfer in the tube again more walking and stairs.
With four of u , it is certainly worth a taxi, imo.
Hopefully u will not be using a taxi during peak hours, which slows things a lot.
Splurge enjoy your visit without fatigue.

I used worldtaximeter.com to estimate the fare from Hangar Lane to the Tower leaving at 9 am and the fare came out to be £57. The daily cap for the oyster card in zone 1-4 is £9.80 so you can see how much more a cab will cost. I stayed in Ealing last year so I know it’s about a 30 minute tube ride to central London. Maybe you can take the tube for the commute into London and take cabs between the sights you want to see to save money? Of course, if your budget will allow for the expense then definitely take the cab. You can also try Uber. I’m a firm believer in “cabbing it” so do what’s best for your situation. .

I would consider the buses. It only takes a little extra effort to learn the bus system. It is actually quite simple. The kids would love it especially if you happen hit a double decker but those are going away.

Another rec for the buses. The Transit for London website has a comprehensive map combining the tube system with the bus lines which is worth downloading. When we were there in 2012, we used the buses extensively, only using the tube a few times. I planned out our bus routes the nights beforehand and we got around with no problems.

My husband and I just got back from London and we used bus, tube, taxi and water-taxi to get around. We especially enjoyed bus travel, since we could sit on the upper level of the doubledecker bus and see the various neighborhoods we were going through. The Oyster cards were easy to use, even on the water-taxi. Specifically, after touring the Tower of London, it is a short walk to the pier on the Thames where we boarded the water-taxi and took it back to the Westminster pier.

Uber is much cheaper than black cabs but becareful of surge times
Another competitor to Uber is Addison Lee
I suggest download app of both and compare prices before calling a cab
Watercabs using an oyster card are fun but ate more expensive then the underground or bus.

Hangar Lane is an expensive taxi ride into central London and can be subject to lengthy traffic delays. Black cabs are more expensive in the evening and at weekends. If you can manage it, I would take the tube or bus into central London, then take a bus or taxi if needed between sights. Take a taxi home if needed. The cost will depend on how much traffic you get stuck in, but based on shorter fares that I have had in central London, I would guess at £60-70 each way. A local mini cab company maybe cheaper. The Tower of London to the Globe will be c £15 in a taxi.

Hangar Lane is reasonably close to the end of the tube line for you to get a seat if you don’t travel peak times. Taxi fares will be more expensive in the rush hour.

I know Hanger Lane well... don’t get your expectations up, it’s not a pretty part of London, but, Hanger Lane in on the Central Line, the best tube line, and you’ll be in to town in no time. 5mins along the road is Park Royal on the Piccadilly Line, which may be useful depending on where you are travelling too.

As an illustration Hanger Lane to Tower Hill by bus would be around 2 hours on a good day with a number of changes.

A cab would be of the order of an hour plus, maybe a little less if the traffic is behaving but don't count on it.

The quickest route by Underground would take around 45 minutes, but that includes changing at the Bank / Monument complex which has up to a 10 minute walk in it.

Regarding cost, your 10 year old will travel free and your 12 year old at half adult price if you get a young visitor discount applied to an Oyster card.

You are really not staying in an optimum location for the range of places you want to visit in quite a compressed time though.

Thank you all so much! Lots of good tips to start checking out. It probably was unwise to stay so far out, but we’ve already paid for it, so I think we’re stuck there. The flat is on Bispham Road, and has excellent reviews, so we’ll keep our fingers crossed. I think we’ll do okay. We obviously know we’re just getting a quick taste of London, and I have no doubt we’ll try to get back someday and spend more time in the city. It sounds like public transportation will be the way to go for most of it, though we may plan to take a taxi back ‘home’ after Hamlet...

Laura

Before you head out, either download the CityMapper app to a mobile device or visit their website here.

You can enter from any address to any address in the area. To show you how accurate and comprehensive a tool it is, I chose the address of a fish & chip shop in the area of Hangar Lane Tube station and had an imaginary person travel to the Tower of London. On a Monday at 8.50am. It shows how long the walks to and from the stations are, what color and name and direction of Tube lines to catch, how long each leg of the journey is, how many stops the trains will take so you have a good idea when your stop is coming up... 58 minutes door to door. The app also says just getting off the Central Line at Bank station and walking the extra 13 minutes also takes 58 minutes. Leave at 0850, arrive at 0948.

The app also says that, based on the travel times of the thousands upon thousands of people that use the same app (and their computers can stitch together an accurate estimate based on user locations), a taxi or Uber would get you to the Tower at 0952, taking 3 minutes more.

London (public) transit journey planner: https://tfl.gov.uk/plan-a-journey/
You can set "preferences" to prefered travel modes (e.g. bus) and "routes with least walking".

For taxi cost: https://tfl.gov.uk/modes/taxis-and-minicabs/taxi-fares
You can use Goggle Maps to estimate the distance and time of travel by automobile.

The link Edgar gave you above TFL etc. is a great link. Please try to use it to see if buses are an option for you. The buses are easy to use, cheap to use, and while you’re on the bus you get to look around and see everything, unlike the tube. Sightseeing all the way—And what is more London then a double decker red bus?

(T f l stands for transport for London )
That is the official transit website but you can do almost the same thing by going onto Google Maps right now, putting in the address of your apartment and putting in one of your destinations you can select “bus” (rather than walk or drive )and you can see exactly how long it will take and the route. And your teens can help you do this! Private message me if you need help.

Have a great trip !

Seconding, thirding, etc., suggestions to use the TFL site and Citymapper to plan your expeditions. Especially useful for finding out how far the walk to your destination is after the last leg of the Tube/taxi/bus/train rides.

Getting around inside some Tube stations can involve a surprising amount of walking. So, if reduction of walking is the objective, going by taxi (or Lyft, Uber, etc.) probably wins, and provides the closest approximation of door-to-door service.

Going by car might be quicker than bus or Tube, or it might not.

Central London transport is overtaxed during rush hours. I recommend scheduling something else -- like meals -- while all that is going on.