W&G Investments - a consortium of well-known City names, led by former Tesco finance director Andy Higginson - tabled its formal proposal for the RBS branches after listing its shares on the Alternative Investment Market (AIM) in order to raise an initial £15 million to fund its bid.
It suspended the shares until the outcome of the auction is known.
If its bid is successful, a raft of fund managers would use the listed company to plough in cash to complete the acquisition of the branches, which are being offloaded by RBS in order to meet European rules on state aid.
It is thought a decision could be made by RBS by the end of the month, when it will choose between the bidders or a possible flotation, which would see it follow in the footsteps of fellow state-backed player Lloyds Banking Group.
W&G - named after the Williams & Glyn's brand being sold by RBS in conjunction with the branches - is one of three potential buyers, alongside Corsair Capital, which is working with US private equity firm Centerbridge Capital, and a joint bid from AnaCap and Blackstone.
W&G is proposing to pay £1.1 billion upfront for the branches with a potential ï¿½400 million due later, depending on the performance of the branches.
The book value of the RBS branch assets is £1.55 billion and it has a total loan book of around £20.5 billion, according to W&G.
Mr Higginson - chairman of W&G, who also ran Tesco's banking operations - said: "We believe that our approach will enable the creation of a strong challenger bank which will focus on delivering excellent products and service to both corporate and retail customers."
But it admitted in its listing documents that any deal with RBS could take two years to complete, due to the complexity of separating the branches.
The consortium, which has been in talks with RBS since the beginning of the year, includes a raft of top fund managers and pension funds, including Schroders, Threadneedle, Aviva Investors and Lansdowne Partners.
RBS is under pressure to find a suitable outcome for the branches after a ï¿½1.6 billion deal with Santander fell through last year.
It is also considering selling a minority stake to private equity and institutional investors to kick-start the process.