The leaders also noted that Modi's election had generated a strong hope and excitement in the UK about India's all-round development.
"The visiting leaders conveyed British Prime Minister David Cameron's felicitations to the Prime Minister and extended his invitation to him for a visit to UK," a release from the Prime Minister's Office said.
Reiterating its desire to deepen economic linkages with India, the UK said it was interested in expanding its network of diplomatic and trade offices in the country.
Among other issues, Modi "discussed with the visiting British Ministers ways to strengthen ties in the area of trade, investment, infrastructure development, energy, cyber- security, defence equipment, education and science and technology," the release said.
The UK ministers lauded Prime Minister's "bold" initiative to invite SAARC leaders for the swearing in ceremony of the new government in May, it said.
Conveying his appreciation for the invitation from Cameron, Modi said he "looked forward to an early opportunity for a substantive visit to UK to take the relationship to a qualitatively new level".
He also conveyed his invitation to Prime Minister Cameron to visit India.
Modi noted the many strong links that have created a strong foundation for India-UK relations, especially the contribution of people-to-people ties, the strong and successful Indian diaspora and the generations of students.
The Indian leader also reiterated his strong commitment to develop friendship and cooperation with all neighbours.