Although access to the more famous Shard will cost up to £30 ($53), just across the river the Skygarden at 20 Fenchurch St is absolutely free. Book online for dates up to three weeks in advance. When you arrive for your prebooked slot, you'll go through a quick security check, then a lift will whisk you to the three-storey glass dome, 155m up, where you'll find 360-degree views and London's highest public garden.
• skygarden.london
5 Get cultured
The Royal College of Music, St Martin-in-the-Fields church, the Royal Academy of Music and South Bank's Royal Festival Hall and Queen Elizabeth Hall all offer free music performances at various times and days of the week. At The Scoop London - a 1000-person sunken amphitheatre - theatre, opera, music, dance and film events are free and open to the public, with no tickets or bookings required.
• morelondon.com/events/about
6 Get your skates on
For something completely different, see the city by rollerskate. Every Wednesday night from April 19 to September 20, LondonSkate offers a free two-hour tour of the city along a pre-planned route, pre-approved by local authorities. Usually there are 200-500 skaters taking part, with a team of experienced marshalls and a custom-built sound system along for the ride. Routes vary throughout the season - check the website on Tuesday afternoons for the next day's start point.
• londonskate.com
7 Pay your respects
The "Magnificent Seven" cemeteries were established in the 19th century, inspired by Paris' Pere Lachaise famous burial ground. Found in Kensal Green, West Norwood, Highgate, Abney Park, Nunhead, Brompton and Tower Hamlets, the cemeteries are beautifully peaceful places, with historic tombs and headstones dating back to the 1800s.
Brompton is the country's only cemetery owned by the Crown and managed by The Royal Parks, and is the final resting place of suffragette Emmeline Pankhurst.
• brompton-cemetery.org.uk
8 Stick to tradition
The Changing of the Guard - where the New Guard takes over from the Old Guard - takes place daily at Buckingham Palace between April and July, and on alternate dates between August and March. Aim to arrive no later than 10.30am to get a good spot - the ceremony will start at 11.30am sharp.
The Ceremony of the Keys - the traditional locking up of the Tower of London - has taken place every night for the past 700 years. Tickets are free but can only be booked online and are in such high demand it's now sold out until February 2018. If you're planning a trip for next year, make sure you book well in advance.
• hrp.org.uk/tower-of-london
9 Get political
The House of Lords and House of Commons are open to the public and free to attend. You'll have to go through airport-style security but once inside, you'll be able to see Westminster Hall, St Stephen's Hall and the Central Lobby, before making your way up the many stairs to the public gallery, where you can stay for as long - or as short a time - as you like.
• parliament.uk/visiting
10 Be on TV
The BBC is the largest provider of free TV and radio tickets in the UK and is always looking for studio audiences for its shows. You can apply online and you'll be notified via email if your request is successful. Audience tickets for many other popular TV shows are handled by SRO Audiences, including The Graham Norton Show, Would I Lie to You and The Voice UK.
• bbc.co.uk/showsandtours/shows; sroaudiences.com
Staying safe in London
MFAT's Safe Travel website recommends New Zealanders visiting or living in the United Kingdom should "keep themselves informed of potential risks to safety and security by monitoring the media and other local information sources. We recommend following any instructions issued by the local authorities and exercising a high degree of vigilance in public places. United Kingdom authorities have urged the public to remain vigilant and to report any suspicious activity to the police."
Register your trip on safetravel.govt.nz and note down the contact details of the New Zealand High Commission - 80 Haymarket, London, ph +44 20 7930 8422, email: consular@newzealandhc.org.uk, online: nzembassy.com/united-kingdom; facebook.com/nzhcuk