Q. In a bid (for me) to save money for the summer holidays, my seven-year-old son and 10-year-old daughter will be staying at home in London this half term. However, they – and I – don't want to stay indoors all week. Is there anything we can do that won't cost money, such as free activities or events?

P Watkins, via email

A: Your children have probably had their fair share of science, history and art museums, but there is plenty more to keep them occupied during half term that won't rack up the admission fees or rely on good weather. Don't forget that up to four children, aged five to 10, can travel for free with an adult on buses, trams, Tubes and the DLR. Just present your adult ticket or Oyster card at the station.

The bank holiday kicks off this weekend with east London's Victoria Park being converted into a "Paradise Garden" (020-8691 1372; www.paradisegardens.org.uk). The two-day festival, which runs from 1-10.30pm today and tomorrow, aims to capture the essence of "parks as pleasure gardens", a centuries-old concept that promoted parks as a community meeting place, as well as a green space. Expect live music, street art and a village fête as well as child-oriented performances, including Albert the Ogre. There is only a charge for steam fair rides, the food and craft market, and circus performance, otherwise everything is free.

On Bank Holiday Monday, Trafalgar Square celebrates Africa Day with an afternoon and evening of music, dance, craft and food from around the continent ( www.london.gov.uk/mayor/culture/africaday), which is also free to attend, from 1-8pm. Hold back on bringing a packed lunch and splash out on some of the local foods, such as jollof rice and suya (a type of kebab).

Over in Covent Garden, the Royal Opera House (020-7304 4000; www.royalopera.org) is opening its doors to families on Tuesday, to reveal its behind-the scenes secrets. Activities will include a ghost tour and the opportunity to play instruments as well as take part in demonstrations with the production team. Free tickets are available on a first-come, first-served basis from the box office, from noon on the day.

On Wednesday you could spend the day in the Barbican at the Museum of London (0870 444 3852; www.museumoflondon.org.uk), where at 11am children can enjoy the "spicy scents in Brick Lane", an activity course that explores the cultural diversity of London through creating street signs relevant for this "Banglatown" artery. After this, explore the adventurous side of the animal world with the "Unexpected Heroes" storytelling session at 1.30pm where children can discover how animals helped the war effort.

If the sun is shining, you could take your children to Greenwich Park on Thursday. The Gentle Giants of Greenwich Park guided tour ( www.royalparks.org.uk) visits the park's bigger trees and their inhabitants and starts at 10.30am. Afterwards, you can saunter down the hill to the National Maritime Museum (020-8858 4422; www.nmm.ac.uk) for the "Give us back your 11 days" event, part of the Oceans of Discovery exhibition. This half-term programme documents how 11 days were knocked off the calendar after riots in London in the 19th century. It starts at 2pm.

Given that you're keen to save the pennies, a visit to the Bank of England Museum (020-7601 5545; www.bankofengland.co.uk/education/museum) in London's Square Mile might be apt on the last day of half term. Your children can have a crack at safe-breaking or create a mosaic based on the intricate patterns of the bank's ground floor.

Also on Friday is the last day of "Nasty Nature" at the Grant Museum of Zoology (020-7679 2647; www.ucl.ac.uk/museums/zoology), at UCL near Goodge Street. Children can explore how animals and creatures defend themselves – real animals will be present. The afternoon session starts at 1pm (finishing at 5pm) and there is no need to book.

For more ideas on what to do and see in the capital this half term, contact Visit London ( www.visitlondon.co.uk).

Send your family travel queries to The Independent Parent, Travel Desk, The Independent, Independent House, 191 Marsh Wall, London E14 9RS, or e-mail crusoe@independent.co.uk