Blackman was a British Republican, a member of the Liberal Democrats and was previously a member of the Liberal Party, campaigning for the party at the 1964 general election. She declined a CBE in 2002, as she felt that as a republican it would be hypocritical to accept the award. She publicly supported changing the British electoral system from first-past-the-post to alternative vote for electing members to the House of Commons in the Alternative Vote referendum in 2011.