Indian Prime Minister Narendra Modi was greeted with jeers and placards reading "Modi go home," as he arrived in London on Wednesday for talks with UK Prime Minister Theresa May.

Modi is under fire back home over the rising number of rape and sexual violence cases. Critics have accused the government of failing to protect women in the country.

Modi later responded during an interaction with the Indian community in the UK, saying the rape cases were "a matter of great concern," had brought "a shame" on the country and called for the perpetrators to be outed.

Read more: Opinion: Rape becomes a political tool in India

The demonstrations in London follow the several protests that erupted across India over the past week as the latest rape cases were reported. In a case that shocked the nation, an 8-year-old Muslim girl from the northern state of Jammu and Kashmir was kidnapped, drugged and raped repeatedly for several days before then being murdered.

In another case, a state lawmaker from Modi's Bharatiya Janata Party stands accused of raping a teenager. Authorities refused to take action until earlier this month when the girl threatened to set herself on fire. Her father died soon after from injuries sustained while in police custody.

Modi last week expressed his outrage and promised justice. However, the numbers of reported rape cases in India have risen dramatically since he assumed office in 2014. The 40,000 reported rapes in 2016 marked a 60 percent increase since 2012. Some 40 percent of India's rape victims are children.

"The Indian government are doing nothing, and you feel sorry for the families because of the total injustice of it all," Navindra Singh, an Indian-born lawyer who lives in Britain, told the Reuters news agency. "He has been in power for four years now and there has been no policy change to help protect women and children."

Modi embarked on a four-day state visit to London this week, where he will attend the Commonwealth Heads of Government Meeting (CHOGM).

Read more: #MeToo in India: 'Women's rights need more than just a social media campaign'

May and Modi affirm post-Brexit assurances

Meeting with May at the prime minister's residence at Downing Street, Modi told his British counterpart that the UK would be as important to India when it leaves the European Union as it is now.

"Prime Minister Modi said there would be no dilution in the importance of the UK to India post-Brexit," May's spokeswoman said in a statement. "He said the City of London was of great importance to India for accessing the global markets and would remain so."

May used the meeting to once again reassert that the UK remained committed to global trade and investment, despite opting to leave the world's largest trading bloc.

Read more: Outshining a former colonial master: India's economy to surpass Britain's

The UK is due to withdraw from the EU in March 2019, but has negotiated a 21-month transition phase during which it will gradually decouple from the bloc's laws and regulations.

According to the statement from Downing Street, May told Modi that the "implementation period agreed in March gives Indian companies and investors the confidence that market access will continue on current terms until the end of 2020."