Investors withdrew £700m from funds managed by Invesco in June.
A substantial majority of the outflows, about £400m, came from two funds, the Invesco High Income fund, which is run by Mark Barnett, and the Global Targeted Return fund, which is an absolute return fund run by a multitude of managers.
Mr Barnett has run the £6.7bn Invesco High Income fund since 2014, when he took over from Neil Woodford as fund manager and head of UK equities at the firm.
Over the past five years, the fund has returned 13 per cent, compared with 34 per cent for the average fund in the IA UK All Companies sector in the same time period.
The fund is invested in many companies that are exposed to the UK domestic economy, and this part of the UK market has struggled to perform in the wake of political uncertainty surrounding Brexit.
Bhavik Parekh, analyst at Morningstar, said the rate of redemptions from the Invesco High Income fund has been constant at this level for the five years Mr Barnett has been at the helm of the fund.
Meanwhile the £11.2bn Invesco Global Targeted Return fund has lost 1.91 per cent over the past year and 0.42 per cent over the past three years.
In both cases this represents a worse performance than that of the IA Absolute Return sector in the same time period, which has returned 0.22 per cent over the past year and 3.76 per cent over three years.
The fund is managed by David Jubb, David Millar, Richard Batty, and Gwiilym Satchell.
A representative of Invesco said the outflows in June have not been higher than in recent months, across any part of the business.
They said: "We haven't noticed a particular increase in outflows recently, and there are no plans to change the way those funds are run at the present time."