Connections will be subsidised by adverts and business
The fund is run by Freerunner, a company that installs wi-fi hotspots.
The firm has said it will install 50 access points in communities across the UK, "no matter where they are".
Earlier this year, the government made a pledge to ensure that every home in the UK can access 2 Megabits per second (Mbps) broadband by 2012.
A study commissioned by the BBC earlier this year suggested that some three million homes currently have speeds of 2Mbps or below.
The government's Digital Britain report has proposed that every citizen, with a fixed-line phone, will pay 50p per month to pay for the roll out of faster, next generation networks.
"The challenge with the digital divide is how to find people who need connectivity and then how to pay for it," said Alex Salter, co-founder of broadband measurement firm SamKnows, which are not part of the project.
Free model :
Freerunner has launched its competition to find communities which are currently offline.
"A big slice of people across the UK cannot get access to the internet," explained Owen Geddes, CEO of the firm.
The company has offered 50 communities a free connection for a minimum of 12 months.
Mr Geddes said the firm would use whatever technology was necessary - including satellite and mobile broadband - to make sure a winning community was connected.
The connection will be paid for by a combination of advertisements and corporate sponsorship.
Community members have been asked to submit 150 words by 25 September explaining why they need a connection.
The winners of the competition will be announced on the 1 October.
The firm is also working with charity website JustGiving to provide net access to 500 charities across the country.
Freerunner already offers free-to-use access points in community venues across the UK. It subsidises the free services through targeted advertising and by providing connections in venues and commercial settings, such as coffee shops.
