If you’ve hired Hampton Court Palace for your Global Investment Summit, and have King Charles lined up to serve drinks afterwards at Buckingham Palace, it is obligatory to publish a large number to demonstrate that the show was a complete triumph and the UK must be “one of the best places in the world to do business”.

Here it is: £29.5bn of new foreign investment, a figure the government reminded us is three times the sum Boris Johnson was able to champion at his equivalent summit in 2021. One can also admire the precision: £29.5bn invites less suspicion of smoke and mirrors than a round number such as £30bn.

But what is this money that has been “committed” and “pledged” at the summit, or “galvanised” by it? That is the point at which the arithmetic starts to feel a little loose.

Take the largest element – the £10bn over four years from Australian pension fund IFM Investors. This is in the form of a memorandum of understanding with the business department to “identify commercially viable opportunities” in the UK, primarily in renewable energy infrastructure. IFM won’t have signed anything on a whim, but an MoU is early-stage, exploratory planning. Maybe every last penny will arrive, but it’s not as if one can point to an actual project at the moment.

Or look at the £7bn for 2024-28 from Spanish group Iberdrola, the owner of Scottish Power. One can be confident this cash will be spent, but mostly because Scottish Power has invested at roughly that pace for a long time; it cites £30bn in the UK over the last 15 years. The firm is one of the big players in UK windfarms and transmission lines, so it’s hardly a revelation that it will continue to invest in areas where the government is upping incentives to meet net zero targets. Any news, though, from Vattenfall of Sweden or Ørsted of Denmark, the more likely windfarm waverers? Unfortunately, neither Scandinavian firm was on Rishi Sunak’s roll-call of pledgees.

None of which is to deny that £29.5bn-worth of investments and investment intentions is welcome. Nor is it to suggest that the summit shouldn’t happen. There is competition for foreign capital and Emmanuel Macron has his “Choose France” summit at Versailles, so these feelgood events are now part of the calendar for what the UK government called “the world’s A-list CEOs and investors”.

There is certainly no harm in getting the prime minister to tell such an audience about permanent “full expensing” of capital costs, a serious investment-friendly measure in last week’s autumn statement and one the Office for Budget Responsibility said would raise annual investment by £3bn a year compared with the previous temporary policy.

But, for a hard-headed assessment or where the UK lies in the investment stakes, read the 123-page review from the Tory peer Lord Harrington that was also published last week. Short summary: the UK needs a more state-backed “business investment strategy” to attract capital. “The prize is a big one: most of our competitors have about 12% of GDP in business investment (domestic and foreign), our equivalent is 10%. The difference is about £50bn a year,” Harrington said.

Ultimately, it doesn’t matter terribly whether the investment comes from home or abroad, but £50bn is a serious gap to close year in, year out. So don’t read much into a bits-and-pieces multiyear figure of £29.5bn that includes things that would have happened anyway. Calling this summit “historic” is another piece of hype: wait until the trend of underinvestment reverses.