For gross retail sales, the top six managers remained the same as the second quarter, while Baillie Gifford re-entered the top ten to take the seventh spot, pushing Jupiter out of the rankings.
The report noted Baillie Gifford had returned thanks to an 80% surge in new business compared to the previous quarter, with its best-selling fund being the Baillie Gifford European.
There was more shifting within the ranking for net retail sales, as M&G fell from number two to eight, while Royal London AM climbed from sixth to third spot.
Income funds knock Scottish Mortgage and Fundsmith Equity off most bought spots
RLAM was the most successful active manager of the quarter, with the RL Short Duration Gilts and RL Short Term Fixed Income funds among its best-sellers.
"Sales of RLAM's sustainable funds have also proven more resilient than the industry average and the RL Sustainable Leaders fund continues to rank among the most popular ESG funds among retail investors," the report said.
Meanwhile, Canada Life entered the net retail sale tables for the first time, pushing out BNY Mellon for the number ten spot, which the report noted came "following a steady rise in external fund sales as the firm seeks to expand its distribution across the UK retail market".
"Groups which saw their net retail sales increase in the third quarter were HSBC Asset Management, RLAM and LGIM, but for many other managers it was a challenging quarter," the report added.
Square Mile includes investment trusts in Academy of Funds for the first time
While BlackRock maintained its number one spot in net retail sales, it saw its lead over other managers collapse.
In the second quarter, BlackRock's net retail sales totalled £1.9bn compared to M&G in second place with £757m. However, in the third quarter, BlackRock only reached £1.2bn, compared to HSBC AM's £930m.
BlackRock's best seller throughout the quarter was the iShares North American Equity index, which attracted record inflows from retail investors.
Anna Pridham, the report's editor, said: "With savings rates offering a more compelling alternative to financial markets than they have in decades, it is the managers with the right products and the right performance that can attract new investors."