The initial public offering, worth around £20bn, has been delayed until the first half of 2012, reports The Independent newspaper.
The flotation was delayed from the first half of 2011 after its former UK chief executive Antonio Horta-Osorio left for Lloyds Banking Group, taking key management members with him.
Santander UK's business is made up of around 85% retail and commercial banking, with the rest falling under investment.
Until the ICB makes its recommendations and the government accepts them, the lender will not know whether its non-retail services will be part of the flotation or ring-fenced.
However, a Santander spokesman maintained that the lender still plans to float part of the business before the end of the year, subject to the markets.
The ICB is set to publish its final report on 12 September.
