The two countries launched the Dialogue in April last year during Prime Minister David Cameron's visit to Islamabad.
The Dialogue covers five areas of cooperation, including trade, finance and development aid, education and health, culture, and defence and security.
Gilani will be accompanied to Britain by a delegation of senior ministers and parliamentarians, the Foreign Office said in a statement.
During May 8-13 visit, Gilani and his British counterpart will review progress in the Enhanced Strategic Dialogue and launch a trade and investment roadmap to increase bilateral trade to 2.5 billion pounds by 2015.
The premier will also interact with British parliamentarians, members of the cabinet, prominent businessmen and investors and the media.
Gilani will address a community gathering and lay the foundation stone of the Consular Hall in the High Commission.
The Foreign Office said Pakistan and Britain were bound by ties "rooted in shared history, cultural values and people-to-people contacts".
Over a million Britons of Pakistan origin and heritage provide a bridge between the two countries.
Britain is Pakistan's second largest trading partner in Europe and an important source of foreign investment and remittances.
Britain has also been a "consistent supporter" for Pakistan
