Investors briefed by the New York-based financier, who took a surprise 5 percent stake in Barclays in February, said Bramson wanted it to axe all parts of its investment banking operation that did not directly serve corporate clients.
The plan would see Barclays keep its money-spinning M&A advisory business and the equity and debt capital markets teams responsible for leading high-value initial public offerings and bond sales, but cull its cash equities, currency and fixed income trading desks, the sources said.
Spokesmen for Bramson's Sherborne Investors and Barclays, Britain's third biggest bank by market capitalisation, declined to comment.
"The trading businesses lack scale, absorb too much risk capital and deliver too small a return," one of the sources familiar with Bramson's plan said.
"There is a route back to success and respectability for this bank, and this is to focus on the retail bank, Barclaycard and the good bits of the corporate and investment bank (CIB). Management just have to seize it."
Bramson, described as a turnaround specialist on his company website, has until now managed to keep the finer details of his plan to revamp Barclays under wraps since his 700-million-pound investment vehicle - Sherborne Investors Guernsey C - made its stake-building public.
Bramson has a strong record of delivering change at his turnaround targets.
His previous targets have included British private equity firm Electra, where he forced through an overhaul and his Sherborne fund achieved a return of 113 percent as of May 2017.
Sherborne realised returns of 138.4 percent and 143.5 percent respectively from earlier investments in promotional products supplier 4imprint and chemicals business Elementis, where Bramson also pushed through turnaround plans, according to documents accompanying the activist fund’s most recent fundraising last year.
His investment in Barclays, one of the largest activist plays in Europe's banking sector for years, follows a decade of painstaking restructuring by Barclays' board and management, including the sale of its African business and the shedding of 95 billion pounds of risk-weighted assets.
But the bank's share price has continued to languish relative to peers including HSBC and Lloyds Banking Group, which also boast higher dividend yields and return on equity, a key measure of profitability.
Barclays Chief Executive Jes Staley has championed its investment banking division despite its underperformance in recent years.
Staley has recruited a slew of high-fliers from his former employer JPMorgan including Australian investment banking chief Tim Throsby, and more than 40 managing directors charged with restoring profitability to a unit hit by years of upheaval and under-investment in technology.
Recent hirings have focused in particular on the trading business that Bramson is eager to see Barclays cut, highlighting the difference over strategy between the investor and Staley.
The bank has hired Michael Lublinsky from hedge fund Brevan Howard to head macro trading, Stephen Dainton from Credit Suisse as head of equities and Guy Saidenberg from Goldman Sachs as head of Sales. Staley has highlighted the trio by name as key to improving its profits.
The three all have internal mandates to hire more staff and are under intense pressure to boost revenues to justify the investment in the markets business, according to two sources familiar with the matter.
It is by no means clear that other Barclays investors are in favour of jettisoning the bank's trading activities.
Some shareholders told Reuters they believed Bramson might be underestimating the challenge of stripping out the investment bank's underperforming units without hurting stronger parts.
Others feared the move could send some corporate clients into the arms of rivals that could offer them a full range of investment banking services, rather than just the higher-margin business Bramson is keen to focus on.
Such doubts are shared by one of Sherborne's largest investors.
"I am pretty sure returns in Cash Equities are fairly rubbish but it's very hard to do ECM (equity capital markets business) and some M&A activities without it," he told Reuters.
"I think the Markets bit of Barclays CIB is more profitable than he thinks it is, if anything it is the Commercial Bank that is the laggard," he added.
One of Barclays' 20 largest shareholders said Bramson's plan would trigger significant upfront costs and risked reducing revenues even further.
"Closing down large parts of the investment bank would probably be extremely expensive and no doubt mean dividend and buyback restrictions being imposed by the Prudential Regulatory Authority for an extended period given the risks," he said.
(Editing by Mark Potter)
By Sinead Cruise, Ben Martin and Lawrence White