The Building Societies Association is calling for the cash Isa allowance to be doubled to £11,520 in a major overhaul of the system.
Savers can put up to £5,760 of their annual £11,520 Isa allowance into cash or the entire amount into stocks and shares.
The BSA is also calling for the Government to introduce cash incentives for first-time Isa users, which it says could be identified by HM Revenue and Customs through national insurance numbers.
The trade body suggests this would see the Government matching individuals’ contributions by 50p in the pound.
For example, if an individual used the full Isa allowance of £11,520 the Government would add an extra £5,760.
The trade body also wants to see child trust funds to be allowed to be transferred to junior Isas.
Speaking at the BSA annual lunch in London today, BSA chairman David Cutter says: “Savers remain the bedrock on which out lending industry is based, and it is therefore vital to encourage and foster a long term savings culture.”