Just Stop Oil said two climbers ascended the two 84m masts on the North side of the bridge about 5am “forcing the police to stop traffic from entering the bridge”
“It is expected that the bridge will remain shut for at least 24 hours,” the group claimed.
It is likely to remain closed through the Monday evening rush hour.
A police stamement added: “The bridge is expected to remain closed through this evening’s tush hour. Traffic is moving but we anticipate your jourmey will take longer.”
“The bridge has been closed while we resolve the incident which we will do as quickly and as safely for all involved," the force said on Monday.
“It does mean that we have had to close the bridge to traffic, but a diversion is going to be put in place through the tunnel.
“This is likely to cause delays throughout this morning and this incident may take some time to resolve due to the complexities of safely getting people down from height."
The bridge is expected to stay closed through this evening's rush hour.
However, a contraflow's in place through the tunnel.
Traffic is moving but we anticipate your journey will take longer than usual so please plan ahead. pic.twitter.com/0Rsm6nFY03
— Essex Police (@EssexPoliceUK) October 17, 2022
By 6am on Monday, the force said there were "delays of around 60 minutes".
National Highways East wrote on Twitter that there were "60 minute delays with 3 miles of congestion on the approach".
Monday’s actions follow over two weeks of continuous disruption by supporters of Just Stop Oil. The group said there has been more than 450 arrests.
The group is calling for the government to halt all new oil and gas licences and consents.
The A282 Dartford Crossing is currently the only way to cross the Thames east of London by road.
The 2.8km-long (1.7 mile) QEII bridge southbound, and two 1.4km-long (0.8 mile) tunnels northbound link Essex and Kent.
The A282 also connects directly at both ends with the M25 London Orbital Motorway, one of the busiest motorways in Europe.