Mrs May, who will host a Downing Street reception on Wednesday night to celebrate Mrs Cox's legacy, said ministers would produce a cross-government strategy to combat loneliness later this year.
A study by the Co-op and the British Red Cross showed more than nine million people often feel lonely.
Age UK says 200,000 older people have not had a conversation with a friend or relative in more than a month and Scope, another charity, says up to 85 per cent of young disabled adults feel lonely.
Last month's report from the Cox Commission identified new mothers and refugees as groups potentially vulnerable to isolation.
Professor Jane Cummings, the chief nursing officer for England, said loneliness could have a 'devastating impact' on mental health and increase the risk of premature death by a third.
Miss Crouch, who will combine the loneliness brief with her role as minister for civil society and sport, last night pledged to honour the memory of Miss Cox.
She said: 'I am sure that with the support of volunteers, campaigners, businesses and fellow MPs we can make significant progress in defeating loneliness.'
Miss Crouch has been asked to 'pull together all strands of government', including the Treasury, the Department of Health and the Department for Work and Pensions.
New funding will be announced to help communities to identify ways they can reach out to the lonely people in their midst. The Office for National Statistics will be asked to devise a way of measuring loneliness to make it easier to identify and alleviate.
Ministers are interested in identifying community projects, taking as a model the cafe for veterans established in Leyland, Lancashire, by Phil Burton.
The former soldier said the venture had started up to provide 'a place to meet and talk to like-minded people with the same day-to-day issues' but had grown to become a place that allowed 'veterans of all ages to get help where needed'.
Labour MP Rachel Reeves and Mrs May's parliamentary aide, Seema Kennedy, worked with 13 charities over the past year to help find solutions for the commission's report.
In a joint statement last night they welcomed the announcement, adding: 'We are really pleased to see that the Government is taking the issue of loneliness very seriously with its prompt response.'