Just cannot find any answers so far(sorry for being that dumb:

- how to buy/rent cheap cell/mobile phones in London (just need it for a week; all calls will be within England but family will be splitted for a little while).

- going to take our 4 y/o girl with us. She is not a novice in museums already and likes it in general but still will need some more age-appropriate entertainment. London zoo, London eye, walking in parks, WHAT ELSE??

- we're going to Stratford-upon-Avon for theather one evening. Is it possible to return to London the same night by train?(end of the show is about 10:45 PM)

Thanks in advance!

Phone - just walk along any main street and go into one of the many phone shops

Child - Buy a copy of Time Out magazine when you arrive. It has a child events section. Or try www.londonfreelist.com

Stratford - weekdays there is a train at 11:00pm but you have to change trains at Banbury getting into London at 2:00am : see www.nationalrail.co.uk

On your second question...
London Zoo is great, ditto for British Museum and Science Museum. Both are favourite of my 5-yo daughter. From London Zoo, you can get a canal boat toward Little Venice. There are many outdoor parks with children's playground. I strongly recommend Princess Di playground in Hyde Park (close to Queensway) though it does get sometimes crowded. I'm not sure about London Eye--the height may be scary, and short people don't get much view unless you hold her up, and you cannot get off in the middle if she does get scared.
Museum of Childhood is good and I liked it, though my kids weren't impressed for some reason.
Kids enjoy simple things--like riding on the top floor of the double-decker bus, and taking a tube.
If you get stuck in rain/run out of things to do, you can always try children's swimming pool and indoor soft play areas at Swiss Cottage leisure centre.

Science Museum for the kid, definitely.

Have you tried resources like:

http://kids.visitlondon.com/
http://www.kidstolondon.com/

I love wandering around Covent Garden. Your daughter might enjoy the buskers who perform there. Toss a coin in when they pass the hat.

When my kids (and, later, grandsons) were small, I'd make a "treasure hunt" for museums. It keeps them moving forward, finding items and learning about them. They LOVED museums because of it! This would be really easy to do now:

It works like this (using the British Museum as an example):
Go on the Internet and cut and paste several pictures from the museum site onto a blank Word doc (mummies, Greek and Roman statues, copper jewelry--whatever you personally would like to seek out). Put the name of the item under the picture. Print it off in Black & White. Let your daughter hold it on a clipboard and circle things as she finds them. She will look at EVERYTHING as she tries to find the objects and, believe me, she'll learn a lot and have fun at the same time!

We took our just-five year old daughter to London a few years ago. She loved the Natural Science museum, Covent Garden (give her a few coins to dole out to her favorite performers), and the Aquarium. She still talks about the Aquarium today. And seeing Big Ben...

The London Eye I'd consider claustrophobia, heights, and the need to pee. Just a thought.

I would not try to do Stratford in one day. Could you all go out for an evening or two? It's a wonderful little town.

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Uncommon Family Travel