David Cameron has condemned the killing of Russia's former deputy prime minister Boris Nemstov as despicable and callous.
The Prime Minister added the Russian people had been deprived of a champion of their rights and that Mr Nemtsov was greatly admired in Britain, not least by Margaret Thatcher.
"I am shocked and sickened by the callous murder of Boris Nemtsov as he walked in the heart Moscow last night," he said.
"This despicable act must be fully, rapidly and transparently investigated, and those responsible brought to justice."
The 55-year-old, who was a fierce critic of Vladimir Putin, died after being shot four times by an unidentified attacker in a passing car in Moscow during the early hours of Saturday morning.
According to colleagues, he was working on a report which apparently included concrete evidence that Russia was directly involved in the separatist movement which erupted in Ukraine last year.
At the time of the attack, Mr Nemtsov was walking along a bridge with a Ukrainian woman, who was uninjured in the shooting. She is now being questioned by police.
Police spokeswoman Elena Alexayeva said: "Citizen Nemtsov was walking with his female acquaintance, who had come from Ukraine, along the Bolshoy Kammeny Bridge towards Bolotnaya Square.
"All of a sudden, a car pulled over and several shots were fired from inside the car. As a result, four bullets hit the back (of Nemtsov) and caused Mr Nemtsov injuries incompatible with life."
The politician had received death threats on social media, but no steps were taken by the police to offer him protection, according to his lawyer, Vadim Prokhorov.
Russia's investigative committee are pursuing several lines of enquiry include Islamist extremist attack and links to the Ukraine crisis.
A senior opposition politician, Mr Nemtsov was an outspoken detractor of Vladimir Putin's administration - and had planned to attend an "anti-crisis march" through the capital on Sunday.
The economist had said in an interview with Russian media: "Every time I called (my mother), she laments: 'When are you going to stop scolding Putin? He will kill you!'"
Mr Putin has condemned the death, which he said looked like a "contract killing" - adding that he will personally oversee the investigation into the shooting.
Meanwhile, the White House has demanded that the investigation is "prompt, impartial and transparent".
President Obama, who met Mr Nemtsov in 2009, described him as a "tireless advocate" for the rights of Russian citizens, and cited his work in fighting corruption.
Garry Kasparov, chairman of the Human Rights Foundation, tweeted: "Devastated to hear of the brutal murder of my long-time opposition colleague Boris Nemtsov. Shot four times, once for each child he leaves."
Widely regarded as the greatest chess player of all time, the political activist added: "Politkovskaya was gunned down. MH17 was shot out of the sky. Now Boris is dead. As always, Kremlin will blame opposition, or CIA, whatever."
According to the Financial Times, Mr Nemtsov had wanted to tackle the stagnant wages and soaring inflation that has blighted Russia's economy in recent times - with the rouble collapsing and Western nations imposing sanctions over the government's involvement in the Ukraine crisis.
"They believe that the embargo on imported foods is America's fault, and they were surprised when I told them no, that was not Obama, it was Putin. This is what we need to make people aware of: the crisis, that's Putin," Mr Nemtsov said.