Imagine for a moment that you’re buying your dream kitchen.

You’re thinking big: eight gas burners, a huge fridge, a wine cooler and enough storage space to hold 12 of everything — ready for some epic dinner parties. But you decide not to upgrade your dining table. It seats two comfortably, so why bother changing it? In many ways, this is what is happening to London.

In 2018, the £15bn Crossrail will (hopefully) finally open, some 75 years after the idea for a major cross-capital commuter line was first proposed. Crossrail will revolutionise how London works. I cannot think of a single potential occupier Exemplar has talked to for years now who hasn’t wanted to be as close to a Crossrail station as possible.

And occupiers have already committed to Crossrail. In Farringdon, the point where the east-west Crossrail route meets the £5.5bn north-south London Thameslink upgrade, Amazon and Goldman Sachs — to name but two — have together taken over 1m sq ft for their new headquarters. Their thousands of staff will be a few minutes’ walk from a direct connection with three of London’s airports, as well as their homes. The same is repeated in Fitzrovia and Spitalfields.

Commuter stampede

When Crossrail opens, figures indicate that around 250,000 people a day will use the line to journey into central London, roughly equivalent to the entire population of Southampton. Most will be commuters, not tourists, which begs the question: where on earth will these people actually work?

Simple maths suggests that 250,000 people translates into around 25m sq ft of office space. There are only five Crossrail stations in central London and the amount of new office space under construction has averaged 7m sq ft per year over the last 10 years. This is low, but nowhere near as low as the current office development pipeline for these markets which, for the whole of 2015-2016, totals just 4m sq ft.

Further ahead, global consultancy Arup forecasts that three Crossrail interchange stations — Bond Street, Tottenham Court Road and Farringdon — will see 250 million passengers a year as London’s population heads towards 10 million people.

The reasons why construction figures are so low are clear to most — we have very limited land, and ultra-high residential values outside the City make offices unviable, plus government planning policy favours residential. But do we need or want more residential in the core when we have spent £15bn on a fantastic new commuter line? Surely better to have offices for people to work in, boosting the economy and supporting the capital’s internationally acclaimed shopping and dining districts.

New buildings alone won’t solve the problem. Developers have to look carefully at existing office stock and question what would happen if we could build taller buildings, or even add to existing structures. I’m not talking about towers; if, for example, you added a single storey along the length of Oxford Street, you’d be adding another 1.5m sq ft instantly — equivalent to the size of the Shard.

Despite London’s high-rise landmarks, we actually live in an extremely low city, with an average building height of 13.6m. This compares to 18.6m in Berlin and 51.3m in Los Angeles. If you head to Paris, most buildings are around six storeys, even in core residential areas. But I promise no matter what building you’re working on or where it is, the first words from a planning officer when reviewing your proposals for the first time will be “can’t you just take a storey or two off?”

London is, of course, a historic city, with more than 11,000 listed buildings in Westminster alone, and this exacerbates the problem. We obviously can’t and shouldn’t touch these properties, but we need to think about how the remaining buildings can be improved and enlarged.

The capital faces an important choice. We can celebrate historic London and say “forget growth” in the centre, let office development happen outside the core, in the suburbs or regions, and accept that London will lose its status as a world-class city in the future. Or we have to adapt and grow.

If we’re demanding more major infrastructure projects for London, then we have to have an economic reason for them, and that’s going to require a change of planning policy, a new set of architectural rules, and a load of guts. The conversation starts now — perhaps it’s one for your next dinner party.