But there have also been fears that banks - caught out by Osborne's surprise announcement in the Budget - haven't been ready to offer the new Isas.
Yesterday the British Bankers' Association was keen to dispel that rumour.
A spokesman for the BBA said: “We have been working hard to get ready for the new ISA regime and been holding weekly calls with our members, fund managers and other providers to prepare for these changes.
“Staff have received specific training and banks have put plans in place to make sure they are ready if there is a surge of customers wanting to move from stocks and shares products into cash – or vice versa."
Savers have also been put-off stashing money in the tax-free wrapper by record low savings rates. The average cash Isa interest rate is now just 1.58 per cent, according to Moneyfacts. A year ago it was 1.74 per cent.
"People have also been looking at alternative homes for their savings, such as peer-to-peer platforms and a number of popular retail bonds," according to Andrew Hagger of MoneyComms.
But the government hopes that today's new flexibility will reverse that. George Osborne said: "Today’s introduction of the New ISAs is a big boost for millions of people, giving them greater economic security by putting aside money in savings.”
