"A morning for diplomacy. After Chinese FM, UK Secy of State for Intrnational Development @patelforwitham calls on PM," External Affairs Ministry spokesperson Vikas Swarup tweeted.
Earlier, Chinese Foreign Minister Wang Yi, who is on a visit to India, called on Modi.
Patel, who arrived here on Friday in her role as a cabinet minister in the new British government of Prime Minister Theresa May, also held meetings with Finance Minister Arun Jaitley and Urban Development Minister Venkaiah Naidu.
She said that Britain was deepening its economic partnership with India to deliver long-term progress.
With Naidu, she discussed ways of how Britain can share its skills and expertise to drive forward India's vision for new smart cities and boost opportunities for new businesses.