The positive results come from 1,030 players and club staff at 24 Championship clubs, who were tested over the course of Monday 25, Tuesday 26 and Wednesday 27 May.
Blackburn later confirmed that Bennett, their captain, had been tested on Monday and was found to have coronavirus, but was asymptomatic.
He will now isolate for seven days and will return to training on June 5 if he does not go on to develop symptoms, the club said.
Bennett said: “I feel fit and healthy. Hopefully this sends out a positive message to the community that perhaps many people have or have had the virus without showing any effects.
“I obviously would never have known if we hadn’t returned to training and taken the tests, because I don’t feel unwell and have got no symptoms whatsoever.
“There seems to have been a lot of hysteria about footballers returning to training, but it’s not a big deal at all. It’s the people who are seriously ill in hospital that we need to worry about, not footballers who are fit and healthy, and who aren’t showing any signs of being unwell.”
The Lancashire club added in a statement: “Having initially submitted a negative test last Friday (May 22), Bennett took a second test on Monday (May 25), which has now provided a positive result.
“The 31-year-old, who is asymptomatic and feeling no ill effects, will now self-isolate at home for the next seven days and provided he develops no symptoms, he will, in line with medical protocols, return to training with his Rovers team-mates on Friday June 5.”
Fulham meanwhile confirmed two of their players had also tested positive, but did not name them due to medical confidentiality.
“Both players, who shall remain unnamed due to medical confidentiality, are now self-isolating in line with league and government guidance,” the west London club said in a statement.
The results, which show that well over 99.5 per cent of those tested were negative, is a significant boost to the Championship’s restart plans, with the competition hoping to resume at some stage next month.
In a statement published on Thursday morning the EFL said: “Those players or Club staff who have tested positive will now self-isolate in line with the guidelines provided by the EFL and only those who have tested negative will be permitted to enter training ground facilities.
“The EFL will continue to make regular and relevant announcements as appropriate in respect of the testing programme to support competition integrity and transparency.”
An earlier round of tests reflected an almost identical ratio to those reported in the Premier League’s second wave of testing, with two players and staff testing positive from a total of 1,014.
On Sunday it was announced that the two people who had tested positive were both from Hull City.
“Medical confidentiality means the names will not be disclosed, and the club asks for this to be respected,” a club statement read.
“The duo, who are both asymptomatic and feeling no ill effects, will now self-isolate for seven days – in line with the protocols set out in EFL guidelines – before being tested again at a later date.
“The Club will continue to liaise closely with the affected personnel and will make no further comment.”
Players at Championship clubs were allowed to return to training on Monday – the first step towards the potential resumption of the second-tier season.