Spending £875 million on educating the 6.2 million people who do not have basic digital skills - the equivalent of £141 per person - would yield "huge" economic and social benefits for the UK, the right of centre think-tank Policy Exchange said.
Around four out of 10 people aged 65 or over do not have access to the internet at home with more than five million elderly people never having used the internet, according to a report by the think-tank.
The number of people aged 85 or over is set to double over the next 20 years, with older people facing the "major challenge" of increased isolation, as families move further apart for work, it said.
One in 10 people are estimated to visit their GP because they are lonely, with research suggesting that lonely adults are more likely to need emergency hospitalisation and early admission into residential or nursing care, it said.
Tackling isolation could prove to be one of the most effective strategies for countering the rising costs of caring for an ageing population, the think-tank said.
The initial investment in training would be offset by savings of around £1.7 billion a year as people moved to digital rather than paper-based and telephone transactions, it added.
Eddie Copeland, the report's author, said: "In an increasingly isolated and fast-moving world it is vital that everyone in society is able to use the internet.
"Being able to simply write an email or access a social networking site could provide older people with a way to stay connected to their friends and families."
Andrew Kaye, head of policy at Independent Age, a charity which offers advice and support to older people, said: "Encouraging and enabling people to go online could be one really useful means of tackling loneliness - but it's not the only way. To those without technology a trip to the local post office or real human contact is just as important."