Just how dire is the London stock market? It depends who you ask. Of course, the FTSE 100 index is on the rise. It closed at another record high on Friday: 9,491.25. And one senior banker in the City thinks much of the doom and gloom around London is overdone. Capital markets are open and functioning pretty much how you want them to, he says. As for the stock market, “it’s batting singles and twos,” he adds. “What we need is a few fours and sixes.”

For those stumped by the cricket analogy, the translation is roughly: we’re doing OK but we need a few big deals, especially in the area of initial public offerings (IPOs) — once the bread and butter of the City but now a rare feast.

• IPOs signal turning point for City as FTSE closes at record high

Is salvation at hand? The last week or two has brought a small flurry of activity. Take Metlen, the Greek mining and metals vehicle that took a listing on the FTSE 100 in August, valuing it at £5.9 billion. Or Princes Group, the tuna-to-vegetable oil vehicle, which is making a £1.5 billion debut imminently.

Then there’s Beauty Tech Group, a £319 million purveyor of wellness products known for its red-light face mask. And last week we saw the unusual dual listing in New York and London of Fermi, a start-up that wants to build power stations to fuel AI data centres. A buzzy area, for sure, which has helped it land a toppy £10 billion valuation (its track record in building power stations so far? Zero). Also in the plus column: the float of Shawbrook Bank, reported to be imminent.

As we reported last week, fintech Revolut is studying the Fermi model of a dual US-UK listing, confounding expectations that it would shun its home market of London.

Further help is coming from the unlikely quarter of Uzbekistan, midway through a privatisation programme in which it has favoured London for the potential IPO of its state gold miner (tipped to be worth £4 billion) and now, we hear, its national investment fund (with a putative £1.2 billion value).

Of course, not all of these floats are particularly hi-tech or, dare I say it, sexy. Fintechs aside, they do not entirely dispel the disparaging image of London as a “Jurassic Park” of stocks comprising banks, miners, oil and gas giants and consumer goods makers. But they are welcome none the less.

On the negative side of the ledger, we must place AstraZeneca, and its decision to take a direct listing in New York. While it will keep its foothold at the top of the FTSE 100, its UK shares will be converted into depositary interests — a technical move that means, by a quirk of the system, they will not bring stamp duty in to the Treasury, with a consequential £200 million annual hit to the nation’s coffers.

Reaction to Astra’s move last week was mixed among City types. The more upbeat suggested this was a result for London, and the government, because it forestalled an outright departure. The more downbeat fear that this is a mere staging post to a delisting from the UK.

• Keir Starmer spoke with AstraZeneca boss before listing move to US

At The Sunday Times, our Reviving the City campaign this year has flagged a number of ways for the stock exchange to regain its mojo. While the Financial Conduct Authority and the Treasury have made changes to listing rules — of mixed value — much has been made of the ongoing failure of pension funds to divert more of their cash into equities.

James Wise, a partner at Balderton, which was an early investor in Revolut, believes pension funds should allocate more capital to shares by default — although, like me, he stops short of recommending the controversial “mandation”, which has been mooted by the chancellor, Rachel Reeves. He puts it this way: “The Manchester Stock Exchange was shut down in the 1970s and rolled up and we were told it will all be fine … the money will be in London, but it will still flow to Manchester. And obviously it was the end of the financial industry in Manchester.

“There’s a really stark wake-up call that actually we could lose probably the most productive asset in the whole of the UK, which is our financial sector.”

Trying to get pension funds to invest more in Britain is not exactly a new topic. When Boris Johnson was in Number 10, he and his then chancellor Rishi Sunak called for British investors to embark on an “investment big bang” — although they were more concerned about infrastructure projects than the stock market at the time.

I can’t get around the stumbling block that mandation tests pension trustees’ fiduciary powers to destruction. You can’t be forced to flow money into stocks if you don’t believe they will give the best return to your clients.

• Special pleading over pensions investment is not the answer

There’s another obvious move that could help juice the City: abolish stamp duty on share trading. The Treasury is typically coy about whether this is up for review ahead of the budget, but the UK, which charges 0.5 per cent on share transactions, is an obvious outlier. Among peers, only Ireland charges more, at 1 per cent, according to data from Peel Hunt. France and Hong Kong charge 0.3 per cent; the US, Germany and Australia none.

Abolishing stamp duty wouldn’t be cheap; it raised almost £4 billion for the exchequer last year. Yet that figure can wax and wane depending on the health of the market. Despite the glimmer of IPO activity outlined above, there are still more companies leaving the stock market than joining it. City wags are quick to point out that if this carries on, stamp duty won’t be raising nearly as much as £4 billion in the future. Who knows? Axing it could trigger a few of those fours and sixes we’d like to see.

jon.yeomans@sundaytimes.co.uk