Protesters gave speeches and banged drums outside the Home Office building before setting off.
They then gathered in the road outside the gates of the BAE yard.
Lynn Jamieson, of CND Scotland, was one of those speaking before the march set off.
She said: “The whole industry of nuclear weapons has caused so much harm in the global south as well as the global north.
“UK nuclear weapons were tested on the back door of indigenous people in Australia.
“The whole business of nuclear weapons still has that mentality behind it.”
Earlier, activists dressed as Pikachu gathered opposite the Cop26 conference as climate protests continued in Glasgow.
The giant Pokemon were demanding an end to Japan’s support for coal power.
On Thursday morning, a group called No Coal Japan held up a banner saying “Japan, time to end coal” on the opposite bank of the Clyde.
Ocean Rebellion, a sister organisation to Extinction Rebellion, also held a demonstration opposite Cop26.
Activists wearing giant fish heads protested against bottom-trawling fishing, saying it releases “blue carbon” which is harmful to sea life.
Ocean Rebellion co-founder, Sophie Miller, said the group wanted to see the Marine Stewardship Council take tougher enforcement action against the fishing industry.
She said: “They need to actually enforce the rules, there needs to be a body that regulates the Marine Stewardship Council.”
It comes after several demonstrations took place in Glasgow on Wednesday, including an Extinction Rebellion march through the city attended by hundreds.
On Wednesday evening, Police Scotland said five arrests had been made at the demonstration, including two after an incident where officers were sprayed with paint.
Assistant Chief Constable Gary Ritchie said: “We will provide a proportionate policing response to any protest and it is therefore extremely disappointing that officers were assaulted by having paint sprayed in their faces.
“These officers were simply doing their job and trying to protect people and keep them safe.”
Hundreds of activists were stopped at St Vincent Street after marching through the city, before being allowed to go towards the Cop26 site within a police cordon.
The Cop26 Coalition, which is made up of a number of civil society groups, said the police action had been “heavy handed” and called for the First Minister to intervene.
Speaking on behalf of the coalition, Mary Church, of Friends of the Earth Scotland, said: “As we hurtle ever closer to climate catastrophe and negotiators determine the fate of billions around the world, it is absolutely vital that civil society movements from Scotland, the UK and around the world are able to make their voices heard on the streets of Glasgow.
“Yet police are using intimidatory tactics and abusing their powers to stifle the fundamental right to peaceful protest.”
On Friday, thousands are expected to march through Glasgow with the Fridays for Future movement founded by Greta Thunberg.
Saturday will see another large march from the Cop26 Coalition, with organisers saying tens of thousands are expected.