HEAT seems to bounce off the Thames, and the landmarks are visible all the way to the hazy horizon, as the glass pod inches its way above the silvery river.

London, laid out before us, looks just like we left it – give or take the odd skyscraper and the scaffolding surrounding Big Ben, which is undergoing a £61 million repair.

“It’s the bell which is really called Big Ben, you know,” says the 14-year-old, knowledgeably. “The clock tower is called the Elizabeth Tower after the Queen. While the tower is being fixed, there will be no bongs.”

“Where have the bongs gone?” wonders the 10-year-old, peering out of the window, as if he might see them floating by.

We are on the mighty London Eye, admiring the view, taking in the sights at height.

Staying with friends in the leafy neighbourhood of East Finchley, a convenient few stops from the centre of town on the Northern Line, we are cramming as many family-friendly activities as possible in to our short summer break in the city.

The boys are entranced by this giant Ferris wheel-like structure, and its snail’s-pace journey into the sky. It takes around 30 minutes to do one loop and the uninterrupted views of the city are fantastic.

It’s a lovely, peaceful pause in our action-packed holiday – nothing else in London goes at this speed.

Short breaks in the capital, particularly for Glasgow families, are much easier to achieve thanks to Virgin’s West Coast Line – the four-and-a-half-hour trip means travel no longer takes up a massive chunk of precious holiday time. And, as anyone who has ever driven to London with a packed car and small children will know, taking the train is much less stressful.

Our boys are bigger now, but they still get a thrill out of train travel. For London especially, they love the journey down followed by the station-hopping and line-switching that comes with travelling on the Tube. (In fact, by the end of our trip, they are satisfied to announce we have travelled on a total of 21 trains, underground and overground.)

Our journey to London was smooth and fast, but walking out of the comfortable air-conditioned carriage on to the platform at Euston was a shock to the system.

“It’s like walking into a hairdryer, full blast, in your face,” marvelled the 10-year-old.

London in a heatwave is hot and sticky and busy and exciting. The city sweeps you off your feet, from the moment you step off the train, bundling you along in crackling haste before you have time to catch your breath. Coming here is always an adventure. Our natural parental caution is at peak levels – since the last time we brought our children here, there have been two terrorist attacks, on Westminster and London Bridges – so we are more vigilant, certainly, although keen not to let any sense of unease overpower the joy of being back in one of our favourite cities.

Before our trip on the Eye, our first stop was Windsor, for a mini-break-within-a-break. Used to trundling through on the shuttle bus to Legoland, we have often thought it would be nice to spend a day or two exploring, so this time we did.

We hopped on the very clean, very pleasant South Western Railway service from Waterloo, a 55-minute journey to Windsor and Eton Riverside. We stayed in the Travelodge, perfectly placed and cheerfully cheap, which meant everything was within walking distance.

Windsor is beautiful, a peaceful historic town with pretty river walks and the largest and oldest inhabited castle in the world. The aftermath of That Wedding is everywhere – you can have your photograph taken beside a giant Harry-and-Meghan LEGO mosaic in the shopping precinct, or pick up a souvenir of their faces on everything from tea towels to tins of teabags.

Windsor Castle is magnificent – a “proper” castle, agree the boys, where ACTUAL Royal people live. It is huge and fascinating, and we spend a few hours taking in the pomp and ceremony. There are plenty of family activities and it’s fun to hear about the murder holes in the walls, and the massive Doll’s House built for Queen Mary.

After the grand, peaceful surroundings of Windsor Castle, Legoland was a brilliant splash of crazy colour and noise. The park has some exciting new additions for 2018, including a 4D Ninjago movie, a digital aquarium and Ninjago-themed rooms in the resort hotel, but old favourites were the big draw for our boys.

There is so much to see and do it’s impossible to fit it all in to one day trip but we explored MiniLand (the new buildings, such as the Sydney Opera House and the majestic 47,000 brick Taj Mahal, complete with the famous Princess Diana bench, are fabulous), splashed out on cooling water rides such as the Viking River Ride and Raft Racers – the only time I’ve been delighted to be soaked to my skin – and ate pizza and pasta and ice cream in the resort restaurant while we watched the funny, silly, pirate acrobatic show.

Back in the city, we hop on the hop-on-hop-off open-topped bus to continue our sightseeing. The Original Tour, with its Union flag-bedecked buses, has been taking tourists around town for more than 65 years and it’s a fun, fascinating insight into the city and its landmarks.

Archie and Harry are impressed, storing away facts and anecdotes in glee. One of their favourites is the revelation that Cleopatra’s Needle on the Embankment had nothing to do with the Egyptian Queen, but instead was named after the ship – the Cleopatra – which brought it to London.

At night, London becomes less family-friendly, our boys not yet old enough for us to fully embrace the vibrant bar and restaurant scene. But we love a trip to a West End show and, this time, we are about to enter the magical, mysterious world of Harry Potter and the Cursed Child – the two-part eighth story, 19 years after the original books introduced us to Harry, Hermione, Ron and the rest.

Like everyone else at the Palace Theatre, we swore to #KeepTheSecrets, so I can’t tell you any more, other than to say a young Potter-obsessed fan and his big brother sat, gobsmacked as real magic happened on stage in front of them.

Our holiday ends with a couple of restful days in East Finchley. On our way to picnic on Hampstead Heath, we keep our eyes open for Justin Bieber, who has just rented a £108,000-a-month mansion on The Bishop’s Avenue, a street full of magnificent houses hidden behind severe security fences and mature trees.

There is something peculiarly depressing about this sainted street, dubbed Billionaire’s Row and reputedly the most expensive road in London. Many of the houses have just been left to fall into disrepair, neglected by rich owners who don’t live in them. The sight of grand old houses, neglected and weed-infested, lying empty and crumbling when ordinary people elsewhere battle homelessness and food poverty, sticks in our throats. Archie, whose moral compass and social conscience have always been strong, is appalled. Even Harry, whose 10-year-old-head is still full of Harry Potter and holiday fun, is momentarily silenced by the sheer, stupid waste of it all.

On the heath, all outrage is nudged aside in the joy of picnicking. This is proper countryside, just a few kilometres from Trafalgar Square, with one of the best views over London from Parliament Hill. There’s a lot on offer, from wildlife-watching to pond-swimming.

In the tropical temperatures, we stick to the picnic and some Frisbee-throwing in front of Kenwood House (the big white house, you know, in the Julia Roberts/Hugh Grant film Notting Hill?) before relaxing in the sunshine.

Picnics on Parliament Hill, Potter at the Palace, those Eye-popping views of the river and a proper old castle – London has a lot to offer families in search of adventure.

FACTBOX

Travel to London Euston from Glasgow Central on Virgin West Coast costs from £30 standard and £60 First Class single. https://www.virgintrains.co.uk/

Travel to Windsor Eton and Riverside from Waterloo with South Western Railway costs from £26.10, or from £21.10 with the Family and Friends railcard for two adults and two kids. Until September, kids travel for £1. https://www.southwesternrailway.com/destinations-and-offers/offers/livebig

A family room at Windsor Central Travelodge costs from £59 per night in peak season. https://www.travelodge.co.uk/hotels/329/Windsor-Central-hotel

A trip on the Coca-Cola London Eye costs from £27 for adults and £22 for children. https://www.londoneye.com/tickets-and-prices/general-tickets/

A family ticket for Windsor Castle costs £54.70 (for two adults and up to three under-17s) https://www.royalcollection.org.uk/visit/windsorcastle

A family ticket for The Original Tour, which includes a three walking tours and a Thames River Cruise, costs £71.50 if you book online in advance. www.theoriginaltour.com

Tickets for Legoland cost from £32 on selected dates when booked seven days in advance. https://www.legoland.co.uk

Find out more about Hampstead Heath at www.cityoflondon.gov.uk

Tickets for Harry Potter and The Cursed Child at The Palace Theatre, priced from £15 per person per part, are now on sale for the period up to April 7, 2019. https://www.harrypottertheplay.com/uk/ticket-information/