When did you hear of Bitcoin? The first transaction involving the digital currency was just four years ago – believed to be a Briton paying a programmer in Florida for a pizza. But Americans are embracing this form of computer-generated money so fast you can now use it to buy a ticket to the ball game – as well as a flight into space with Virgin Galactic.

What new financial instrument will we be writing about come 2020? We just don't know – and it is this hectic pace of change in finance that poses the greatest challenge to Labour's proposals to break up the banks.

Ed Miliband's argument is that the main problem with banks is they have become more and more concentrated, and that capping their size, and giving two new players an 8% market share each by carving up the existing players, will ensure they start serving us rather than themselves.

Let's put aside the fact that Virgin Money (carved out of Northern Rock) or the new TSB (awarded 4.5m accounts broken off from Lloyds) have hardly turned high street banking upside down. Or that the "big four" has for long been a misnomer, with Santander, Nationwide and Halifax all competing furiously for our current accounts.

There is already a very different revolution going on in banking, but it's not in the branches on our high streets or even in our wallets. By the time Miliband's competition shake-up could come into effect, the current vogue for filling the branch with iPads, the chip-enabled debit and credit cards in your wallet, even contactless payment cards, could look as quaint as writing out a cheque with a fountain pen does now.

Take Zapp, for example. It's a new app that is working with major banks and retailers (WH Smith and McDonald's have signed up already) that from next summer will allow shoppers to pay at the till with their smartphone. Its proponents believe it will allow us all to leave our wallets at home. Then take Zopa. It's the pioneer of peer-to-peer lending, which uses the internet to cut out the banks entirely. It matches savers with individuals who want to borrow, leaving out the bank and offering better rates all round. It has grown rapidly in recent years, joined by rivals such as Funding Circle that use the same model to match savers with business borrowers.

In the US, the biggest peer-to-peer firm, Lending Club, has already sourced $3bn in loans and found an avid backer in Google, which snapped up a stake in the firm last May. And then, like it or loathe it, the technology company that is transforming the financial landscape in Britain is Wonga.com. It has already joined the ranks of the biggest lenders in the UK, handing out one million loans last year.

Mobile banking, after a slow start, has skyrocketed over the past year and with smartphones soon to be ubiquitous across all generations, the forecasts about the end of conventional branch banking no longer look so far-fetched. When Labour talks of breaking up the banks to increase competition and let new challengers into the marketplace, it risks fighting yesterday's battles.

There was once a cosy high-street banking cartel with barriers that effectively prevented customers switching accounts to upstart rivals. But technology makes switching accounts today far easier.

Yet the number of account holders moving their accounts remains relatively low. It is not the real or apparent barriers that deter people from moving their money, nor is it a lack of other places to go – it is an entirely rational apathy. There's very little incentive to do so – a 50-quid bonus here or an M&S voucher there. More independent banks on the high street will do nothing to change that.

There is another part of the banking system that remains deep frozen: lending to small- and medium-sized businesses. And if Labour wants to tackle that then breaking up the existing giants will be merely a distraction. Already, many businesses are tapping the bond market for funds, not through traditional stockbrokers but with online retail bond offers direct to small investors. The market has gone from virtually zero to £1bn last year, according to Capita, and it is projected to grow to £8bn a year by 2017.

Labour is right to want to intervene in the dysfunctional market for small business loans, and to redirect schemes such as Funding for Lending towards manufacturing and industry rather than property. But there are technologically more imaginative opportunities and challenges than simply breaking up the banks.