The penalty, which is RBS's seventh fine in four years, covers mortgage advice given between June 2011 and March 2013 - including seven months when Mr McEwan was in charge of retail banking.
The Financial Conduct Authority first warned the group that its sales advisers at RBS and NatWest were failing to properly explain mortgage options to customers in November 2011, and the bank's own reviews had flagged up problems, but it took more than a year to solve the issues.
RBS told the regulator in July 2012 that it had fixed its sales process - only to reveal four months later that Mr McEwan, who joined the bank in August 2012, was starting a new overhaul.
Two consultancies were brought in to review procedures in late 2012. One of them examined 73 cases and could not find evidence that a single customer got appropriate advice.
"Taking out a mortgage is one of the most important financial decisions we can make. Poor advice could cost someone their home so it's vital that the advice process is fit for purpose. Both firms failed to ensure that their customers were getting the best advice for them," said Tracey McDermott, director of enforcement and financial crime at the FCA.
The watchdog said that just two customers out of 164 in its review were given full and proper advice.
RBS issued 177,000 home loans during the period covered by the fine, though the FCA said there was no sign of widespread detriment to customers because of poor advice.
The bank said yesterday it will contact around 30,000 customers asking them to get in touch if they want to raise concerns about the mortgage they were sold. RBS added that all of its advisers, working in branches and on the telephone, have been retrained since 2012.
"We have worked hard to put things right," said Mr McEwan. "[This] notice shows that we still have challenges to face, but we are determined to take the steps needed to earn back our customers' trust."
The firm set up a working group in November 2011 to try and reform its mortgage sales process, but it contained no executive staff and failed to address the problems.
RBS found that some advisers gave their views on when interest rates would rise during a "mystery shopper" review in 2012.
One adviser recommended a five-year fixed-term mortgage after assuring the customer that rates would "absolutely" rise as high as 5.5 per cent in the near future, the FCA revealed yesterday. The problems were made worse by a computer system that only allowed advisers to write 500 characters on each customer's requirements, meaning there was often no record even if the bank had carried out the proper checks and given good advice.
While City analysts do not expect the £14.5m fine to have a big effect on the bank's finances, the penalty represents a setback to Mr McEwan's pledge to turn the bank into "a company that knows what it means to obsess about our customer".
"The latest RBS scandal will undoubtedly put a dent in how customers view its service as the issues uncovered were particularly grave," said Guy Anker of MoneySavingExpert.com. "What really hurts people is when they are directly affected.
"If banks fail to look after their customers' hard-earned cash they will lose them," he added.
The financial watchdog has handed RBS fines totalling £131m since 2010. The bank has also set aside £3.25bn to cover mis-sold payment protection insurance and £1.3bn for interest rate swaps that were improperly sold to businesses.