London has a host of museums that appeal to children. Below is a list of the primary ones, aimed at entertaining and/or educating children. Workshops, educational story trails, special shows and the like are held at most of the locations especially over the school holidays. For a full listing of kid's events check out Time Out magazine or their children-specific, monthly magazine of Kids day Out.
Bethnal Green Museum of Childhood

Cambridge Heath Rd, E2
Phone:+44 (0)20 8983 5200; www.vam.ac.uk.
Daily except Fri 10am-5.50pm; free.
The museum has many weekend/holiday events and activities. It is most well-known for its collection of historic dolls' houses though there are other items to see.
Horniman Museum

London Rd, SE23
Phone:+44 (0)20 8699 1872
Mon-Sat 10.30am-5.30pm, Sun 2-5.30pm; free.
This ethnographic museum has an aquarium, natural history section and lovely grounds to keep the kids occupied for hours.
Kew Bridge Steam Museum

Green Dragon Lane, Brentford, TW8.
Phone:+44 (0)20 8568 4757; www.kbsm.org.uk.
Daily 11am-5pm; Mon-Fri adults £3, children £1; Sat & Sun adults £4, children £2.
A magnificent 19th century pumping station, it is best to visit on the weekends when the Cornish Beam Engines and the miniature steam railway are in operation.
Legoland

Windsor, Berkshire
Phone:+44 (0)20 870 504 0404
Daily 10am-6pm or dusk; adults £17.50, children £14.50.
Perfect for five to eight year olds, Legoland is a great day out with gentle rides and a relatively tasteful them park. It is very expensive but fun.
London Aquarium

County Hall, SE1
Phone:+44 (0)20 7967 8000
Daily 10am-6pm or later; adults £8.50, children £5
Situated on the South Bank, London's largest aquarium is a very well received by kids who love being able to stroke the (non-sting) rays.
London Zoo

Regent's Park, NW1
Phone:+44 (0)20 7722 3333; www.londonzoo.co.uk.
Daily: March-Oct 10am-5.30pm; Nov-Feb 10am-4pm; adults £9, children £7
The zoo has a children's zoo and a 'meet the animals' section which is popular with kids. The Web of Life building was recently opened at this inner-city zoo to try to redefine itself as eco-conscious.
Natural History Museum

Cromwell Rd, SW7
Phone:+44 (0)20 7942 5000; www.nhm.ac.uk.
Mon-Sat 10am-5.50pm, Sun 11am-5.50pm; adults £7.50, children: Mon-Fri all free after 4.30pm, Sat & Sun all free after 5pm.
Hours of fun can be had at this museum with the earthquake simulator, a 'rainforest', dinosaurs, stuffed animals and plenty of rocks, fossils, crystals and gems.
Pollock's Toy Museum

1 Scala St, W1
Phone:+44 (0)20 7636 3452; www.pollocks.cwc.net
Mon-Sat 10am-5pm; adults £3, children £1.50.
An impressive toy collection, housed above a toy shop, this museum also has examples of Victorian paper theatres sold by Benjamin Pollock.
Ragged School Museum

Copperfield Rd, E3
Phone:+44 (0)20 8980 6405; www.ics-london.co.uk/rsm.
Tube: Mile End. Wed & Thurs 10am-5pm, first Sun in month 2-5pm; free.
Kids quickly realise how easy life is these days when they visit this reconstructed Victorian schoolroom.
Science Museum

Exhibition Rd, SW7
Phone:+44 (0)20 7942 4455; www.nmsi.ac.uk.
Daily 10am-6pm; adults £6.95, children free; all free after 4.30pm.
More interactive, hands-on galleries are being introduced at the museum. These are aimed at kids to get them involved and to understand the workings of science. There are also excellent daily demonstrations and a newly renovated transport wing.
Syon

Syon Park, Brentford, Middlesex
Phone:+44 (0)20 8560 7272
Daily 10am-6pm; adults free, under 5's £3.55, over 5's £4.65, with reductions on weekdays
A great day out for all the family, there's plenty to do and see with the Butterfly House, Aquatic House as well as a miniature steam railway in the beautiful gardens. An indoor children's play area and Snakes and Ladders are also in the park.