President Buhari and Theresa May signed a Security and Defence Partnership and an Economic Support agreement.
Both countries signed two agreements on Defence and Security partnership, as well as Economic Development Forum.
May maintained that there should be no law across the Commonwealth criminalising homosexuality.
Buhari said these unnamed persons are hellbent on looting the country dry.
The President said he was more focused on reviving the economy and fighting corruption.
Buhari will also see some prominent Nigerians residing in Britain.
Since 1952, Her Royal Majesty has seen prime ministers come and go — 13 of them.
David Cameron will resign on Wednesday.