The government is to begin a consultation process to decide whether to give prisoners the right to vote.
Supporters of votes for prisoners say it is an inalienable right
If supported, it could mean inmates would become part of the electorate for the first time in British history.
The move follows a ruling by the European Court of Human Rights which found a blanket ban on prisoners voting was a breach of their human rights.
Crime reduction charity, Nacro, has welcomed the move. It said "barring prisoners is wrong on principle".
Every other western European country already gives some prisoners the right to vote.
BBC political correspondent Norman Smith said ministers were aware the move was likely to be unpopular and politically awkward.
Our correspondent said Britain has always complied with European Court rulings and ministers felt they had to seek a change in the law.
The hope was that following the consultation, legislation could be introduced to give the vote to prisoners serving shorter sentences of between three and six months, he said.
The current UK law dates back to the Forfeiture Act of 1870 which is based on the notion of civic death, a punishment which involves the withdrawal of citizenship rights.
A campaign group called Barred from Voting, set up by the Prison Reform Trust, has been pressing for a review of the law.
Among its supporters are former Conservative home secretary Lord Douglas Hurd, Liberal Democrat president Simon Hughes and Labour peer Baroness Kennedy QC.
They argue that a ban on prisoners voting does nothing to deter them from crime and that voting is an "inalienable human right".
Paul Cavadino, Nacro's chief executive, said: "Depriving prisoners of the vote contradicts the aim of rehabilitating offenders.
"If we want prisoners to become morally responsible citizens, it makes no sense to refuse them the responsibility of exercising the vote."
But opponents say those excluded from society should not have a say over the way it is governed.