The Methodist Church, the United Reformed Church and the Baptist Union of Great Britain are concerned by the humanitarian and legal implications of the CIA-operated drone campaign, which has killed thousands in Pakistan.
They argue that the drone strikes contravene international law and incite radicalism and violence.
Leaders of the Churches have written to William Hague urging him to distance the UK Government from the practice.
Steve Hucklesby, Public Issues Policy Adviser for the Methodist Church in Britain, said: "Whole communities are living in fear of the drones flying overhead. The US administration is, in effect, attempting to rewrite international law in order to justify their action.
"This imperils us all. It potentially sets a precedent for any government to declare war on groups of individuals on the basis of a perceived threat that such individuals might present. All governments have an obligation to persuade others to uphold international law.
"Our own government cannot wash its hands of this responsibility while it is in a military alliance with the United States in the region."
The Methodist and United Reformed Churches expressed their strong opposition to drone strikes during their annual meetings over the summer.
Frank Kantor, the Secretary for Church and Society of the United Reformed Church, said: "There is a legal requirement under international law to identify all casualties that result from drone strikes, under any and all circumstances.
"We therefore call on the UK Government to comply fully with this legal requirement, releasing information on the number of fatalities and publishing a summary of all investigations into civilian casualties."
A protest walk is starting tomorrow at the Elbit Factory in Shenstone, in Shropshire, where drone engines are manufactured.
The seven day walk ends at the RAF base in Waddington, where the RAF plans to base Britain's drone operators next year.
The route passes the Thales Watchkeeper Drone Plant in Leicestershire where the aircrafts' bodies are manufactured.
The walk is taking place to raise awareness of Britain's use of drones.
The Rev Bill Anderson, Methodist District Chair for Birmingham, is joining the walk.
He said: "As Christians we are committed to pursue the path of peace. This is a difficult path and made all the more difficult if our forces are perceived as invisible, disengaged and remote. I hope that in each of the places we stop along the walk, we will gather people together who might want to talk to us about why we are walking. That way we can raise awareness about the illegitimate use of drones."
Stephen Keyworth, the BUGB's Head of Faith and Unity, said: "This is an ethical issue of our time that we must respond to.
"The use of armed drones seems to be seductive to governments as the innocent are not supposed to get hurt. From numerous examples this is clearly not the case and their regular use must be reassessed."