Chief executives of online investment platforms expect their assets to increase by more than £100bn over the next five years.
A survey of the chief executives and directors of a number of DIY investing platforms and robo-advisers, carried out by Boring Money, predicted assets would reach more than £315bn in the period.
This would represent an almost 50 per cent increase on the £209bn currently invested online.
Although this would be significant growth, it still represents a small fraction of the total £6.9trn in assets under management in the UK.
Holly Mackay, founder of Boring Money, said: "Although robo advisers retain a tiny market share today, we think that robo mark 2 has the potential to accelerate growth.
"The focus will shift from the provision of online decision trees leading consumers to a pre-packaged portfolio, and move more towards advice."
She added: "If the banks and life companies can crack this space, this will also fuel growth. But that’s a big ‘If’. They are typically slow and hamstrung by committee-think so this needs to be a story of specialist partnerships and collaboration rather than a solitary offense as in the past."
Several banks are either entering the robo-advice space or are considering their options.
NatWest launched its robo-advice service last year, charging just £10, while HSBC has said it will also launch a service this year and Nationwide will be testing a digital investment advice service in the Financial Conduct Authority's (FCA's) regulatory sandbox.
Meanwhile Lloyds has not specified whether it would enter the robo-advice market but it is one of a number of banks working with the FCA as part of its advice unit, a project aimed at increasing access to low-cost advice.
The Boring Money research found executives were predicting assets under management of between €1trn and €2trn across Europe by 2025.
There was £2.3bn managed by UK robo-advisers as of the first quarter of 2018, with Nutmeg accounting for around half of this.
Martin Stead, chief executive of Nutmeg, said: "Investors in the UK have seen the benefits of being able to manage and access their investments easily online and via apps, and as a result, we’re seeing some of the traditional providers looking at how they can get in on the action.
"At well over 50,000 customers, we are one of the top five fastest growing wealth managers in the UK. These figures from Boring Money reinforce what we have known for years - the future of wealth management is online."