At present the savings accounts offered by the likes of Zopa, Ratesetter and Funding Circle cannot benefit from Individual Savings Account status but that looks set to change.
From next month, the 'peer-to-peer' (P2P) lending market will be regulated by the Financial Conduct Authority, paving the way for a move to allow the 'new banks' to offer tax-free savings rates.
According to a survey by comparison site uSwitch, 84% of consumers say they would not invest their money with a P2P lender. Almost half say they don't know enough about them, while 39% were concerned about lack of regulation.
Last year, consumers loaned £480 million to other individuals and to businesses, a 150% rise on 2012. Business crowdfunding, where individuals buy shares in growing businesses, raised £28m and is already regulated.
But an Alternative Finance Summit in London this week heard that even the biggest players led by Zopa have not yet been able to invest in marketing, in stark contrast to the big-spending payday lenders and comparison websites.
The current savings rates offered by the big three social lenders of 4% to 5.7% would become even more attractive within an Isa wrapper, competing with rates of at most 2.8%.
At present a yield of 4.5% is shorn to 3.6% for basic-rate taxpayers and 2.7% for the growing numbers in the 40% tax net.
"We think that differential will drive massive growth," said analyst Cormac Leech of sector bankers Liberum.
"They could take 10% of the Isa market and it could happen over five to 10 years."
A Liberum report shows that with base rates at the current 0.5%, traditional banks pay fixed-term depositors a maximum 2.8% whilst charging borrowers 7%, earning a margin of 4.2%.
The P2P lenders earn a margin of only 2%, which Liberum says would give them the same advantage even when interest rates start to rise.
Of the big three, Funding Circle, which targets small businesses and has loaned £230m since 2010, offers its savers higher rates to reflect the added risk. But the report says Zopa's 'Safeguard' and Ratesetter's 'Provision Fund' do not equate to a deposit guarantee, and the conference heard from both big players that they would not wish to be covered by the Financial Services Compensation Scheme, which guarantees deposits of up to £85,000 with conventional institutions.
Rhydian Lewis, founder of Ratesetter, said: "It would be a shame if we drifted into becoming FSCS-protected - we would be in a homogenous group with the building societies and banks."
Mr Lewis said survey figures showed that 91% of people had trusted banks in 1987 and the figure was now 19%.
"With trust being the foundation of finance, you have to ask is this a fatal blow to the traditional order?"
He went on: "The average age (of P2P customers) is 40 for borrowers and 55 for savers.
"I feel confident that when people in their 20s and 30s grow older they will see P2P lending as completely intuitive and natural."
Giles Andrews, who created Zopa in 2005, said people could put money into a bank or take much more risk by investing in equities or buy-to-let property.
"Investors are looking for a return on their savings but with less risk and volatility. I think we have the basis for a fantastic consumer brand, what we haven't done is promote it and spread the message, because we have not had money to spend on that kind of thing."
But Mr Andrews said the next two years would be "absolutely pivotal" for Zopa, which raised £15m from institutions in January, and he later told The Herald that Zopa's marketing budget this year would be "in the millions".
Mr Lewis said: "Regulation will help because people will feel there is supervision, but regulation does not stop people losing money, what it does is stop the charlatans and the nightmare scenario where people are not sure whether a website is real or not."
The biggest sites claim lending default rates of 0.2% (Zopa) and 0.45% (Ratesetter) whilst saying their schemes have so far ensured nobody has lost any money.
Consumer group Which? is reserving judgment on the sector but has warned about the use of terms like 'guaranteed' and 'protected'.
Scott Murphy, head of consumer insight, commented: "If you put your money into a bank you are protected by the FSCS, here you are not.
"We are not necessarily saying it is a bad thing but consumers need to be aware it is not the same."
He said one factor in the success of P2P was depressed interest rates. "People are looking at areas they would not have considered five or six years ago….there is also a kind of ethical feeling, a resentment against the banks in terms of trust."
The Liberum report notes that banks are already hedging their bets by beginning to invest in the sector, with Santander teaming up with Funding Circle last year.
They are also under threat from other forms of new technology, such as digital wallets, and money transfer platforms.
The report says Transferwise, a P2P foreign exchange service which matches the currency needs of individuals and charges a modest fee, is 90% cheaper for customers than a comparable banking service.