A majority of US states still use capital punishment for certain crimes. It is not surprising, therefore, that a majority of Americans still support capital punishment for murder. Notably however, support for capital punishment in the US has been in decline since the mid-1990s.
The graph below documents public opinion on capital punishment in Britain. The figures are taken from a 2011 YouGov poll, which to my knowledge is the most recent poll on the issue. A minority of British people, only 38 percent, support capital punishment for all cases of murder. However, a majority support capital punishment for murder of a police officer, murder of a child, murder as part of a terrorist act, and multiple murders. Indeed, a full 65 percent of people support capital punishment for the latter offence.
Does the fact that capital punishment has been completely abolished in Britain therefore imply that we do not have a democratic society? Possibly. But there are of course important limits to the democratic mechanism, which is why many countries have constitutions that safeguard their citizens' fundamental rights. As (among others) Milton Friedman noted, "There is nobody who believes that if 51 percent of the people should vote to shoot the other 49 percent, that that would make it okay."