The funding from the Government's £5 billion Restart Scheme has been welcomed by council leaders who have urged councils to act quickly in getting the money distributed.
Latest figures from the Department for Business, Energy and Industrial Strategy show Bassetlaw District Council had issued £5.8 million in grants to 817 businesses in the retail, hospitality and leisure sectors under the scheme up to the end of May.
It came from a £6.9 million pot given to the council, which leaves £1.1 million to still give away by the end of July.
The scheme, opened in April, was designed to boost the economy ahead of the lifting of restrictions.
It offers one-off grants up to £6,000 for non-essential retail businesses and up to £18,000 for firms in the hospitality, accommodation, leisure, personal care and gym sectors.
Across England, £2.6 billion had been passed on to more than 340,000 businesses by councils up to the end of May, although the figures for six out of the 309 councils were unavailable.
Despite the amounts paid out, business leaders have complained some councils have been too slow to pass on the money applied for by businesses.
Andrew Goodacre, chief executive of the British Independent Retailers Association, said: "This data clearly shows that some local authorities still have money to hand out to hard-hit businesses to help with their recovery.
“The association has already voiced its disappointment in the speed in which some local authorities issued grants. They were meant to be Restart grants, in line with the reopening of so-called non-essential retail on April 12.
"However, we know from our members that some councils still haven’t paid the grants – or did so many months too late - despite having business details to hand from the last time lockdown grants were issued."
Meanwhile, the British Beer and Pub Association said delays in payments had worsened a situation for members already hit by the delay in the lifting of restrictions for indoor hospitality.
A spokesperson added: "With the delay to July 19 for a full reopening of our sector, more support is needed in the form of grants."
At the launch of the Restart Grant scheme, small business minister Paul Scully and tourism minister Nigel Huddleston wrote to councils, urging them to release the funding as soon as possible.
It followed some criticism that councils had been too slow in passing on financial support from other funding schemes such as the Additional Restrictions Grant.
That grant, set up to help businesses which have not benefited from other grant schemes, saw £1.6 billion given to councils and combined authorities, including an extra £425 million at the start of April.
As of the end of May, almost £350 million was still to be allocated, however figures were unavailable for nine councils.
But in Bassetlaw, the council had issued all its a funding pot worth £3.4 million in grants to businesses.
The Local Government Association, which represents the country's councils, said stringent checks had to be done on businesses before payments under the Restart scheme were issued.
A spokesman said: "Councils have had to come to terms with a rapidly changing landscape and guidance with different grants applying to different time periods and lockdowns but are working fast to ensure businesses can receive funding as quickly as possible.”
There have been a number of funding schemes available for businesses over the pandemic.