Video report by ITV News Correspondent Rebecca Barry
British Swimming chief executive Jack Buckner said the move was "a really poor decision" while former Olympian Rebecca Adlington said she was "shocked" by the decision.
Speaking to ITV News, the gold medallist said she was "left wondering why" swimming facilities have not been allowed to reopen given that the pool is "a sanitised environment".
Ms Adlington said the decision has been met with "frustration," adding: "How can I have a pint but I can't go swimming?
"I just see the benefits of swimming outweighing going to the pub!"
British Swimming chief executive Mr Buckner said: "So much great work has gone on to prepare for pools and indoor sports facilities to reopen.
"We can be trusted in sport to respect the rules and do a great job for the nation's health and fitness."
It comes as professional football saw three individuals from two Championship clubs test positive in the latest round of coronavirus testing.
Tests were carried out on 2,858 players and club staff from the 24 teams in the second tier, with the division resuming last weekend.
The English Football League (EFL) said in a statement: "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."
There were no positive results from testing in Leagues One or Two.
Meanwhile there are growing fears of an outbreak afflicting golf's PGA Tour.
Former US Open champion Graeme McDowell has withdrawn from this week's Travelers Championship in Connecticut after his caddie tested positive for Covid-19.
American Cameron Champ has already tested positive for the virus during pre-tournament screening, while Nick Watney returned a positive test during last week's RBC Heritage tournament.
In cricket Surrey have announced plans to host a two-day friendly against Middlesex behind closed doors at the Kia Oval towards the end of next month.
The match raises hopes that a truncated County Championship campaign could take place this summer.
The match is set to take place on July 26-27 and Surrey hope the game is a precursor to "returning to competitive action the following weekend".
In the international game, Sri Lanka have announced their Test series against Bangladesh has been postponed.
The Bangladesh Cricket Board informed its Sri Lankan counterparts that "a conducive environment" has not been found to prepare its players for the tour, which was due to start next month.