While thanking Britain for quipping the Nigerian military, Buhari also appealed to PM May to facilitate more British investment in Nigeria
He said unlike other Nigerian politicians who are already working towards the next poll, he is bothered about the state of the nation.
The President visited May 10, Downing Street, London on the sidelines of the Commonwealth Heads of Government Meeting (CHOGM).
Presidential spokesman, Femi Adesina said Buhari's meeting with May focused on the three main agenda of his administration - security, economy and fight against corruption.
"We campaigned on three major issues, to secure the country, revive the economy and fight corruption," Buhari was quoted as saying.
"We have elections next year, politicians are already preoccupied with the polls, but I am bothered more about security and the economy."
The President added that Nigeria-Britain cooperation is historical.
He said, "People ought to know how they arrived where they are, if they would move forward. It was a mistake for us to have stopped the teaching of history as a subject in schools, but we are returning it to the curriculum now.
"British companies like Unilever, Cadbury, and many others have stood with Nigeria through thick and thin. Even when we fought a Civil War, they never left.
"But like Oliver Twist, we ask for more investments. We are encouraging more British companies to come to Nigeria. We appreciate the support you have given in training and equipping our military, particularly in the war against insurgency, but we want to also continue to work with you on trade and investment."
Speaking on education, Buhari said the government is making more investment in the sector because "people can look after themselves if well educated. In this age of technology, education is very important. We need well-staffed and well-equipped institutions to move into the next generation."
In her remarks, May commended the Buhari administration for "making good progress on the economy", urging it to maintain the focus.
She also said Britain will continue to give Nigeria needed assistance concerning the abduction of young schoolgirls by insurgent group Boko Haram.