Popham is the sole representative of the legal profession on the delegation, which includes business leaders and cabinet members alongside Brown.
The delegation will meet senior government officials and members of the business community as part of continuing efforts to improve cooperation between the U.K., India and China.
The trip kicked off in Beijing on Friday, before heading to India.
Popham has been closely involved with moves to open up the Indian legal market and has previously spoken at the World Economic Forum's India Economic Summit.
The mission comes as hopes for foreign firms to practice in India continue to founder, with the Bar Council of India landing a further blow to hopes of liberalization in November by issuing a joint resolution with the country's state bar councils urging the government not to open up the legal profession to foreign lawyers.
Allen & Overy, Freshfields Bruckhaus Deringer and Olswang are among the London firms to have bolstered their presence in the region in the last year, while Clifford Chance hired corporate lawyer Sumesh Sawhney, formerly a partner with Indian firm Amarchand & Mangaldas & Suresh A Shroff, in 2006.