Environmental activists claim to have deflated tyres on nearly 2,000 SUVs in the past four weeks.
The Tyre Extinguishers said its supporters have taken action in cities across Britain in an attempt to “make it impossible” to own the vehicles in urban areas.
It describes SUVs as “a climate disaster”, “dangerous” and “unnecessary”.
SUVs feature elements of standard cars but are larger and have off-road capabilities such as high ground clearance.
Petrol and diesel-powered models are generally less fuel efficient than cars.
The Tyre Extinguishers describes itself as “leaderless” and encourages people to take action by reading instructions on how to deflate tyres on its website.
People can also print off leaflets to leave on the windscreen of affected vehicles to inform drivers what has happened.
Activists are urged to avoid SUVs “clearly used” by people with disabilities or by tradespersons.
The group, which first took action on March 7, said in a statement: “So far, the Tyre Extinguishers have disarmed nearly 2,000 SUVs in the UK, in Brighton, London, Manchester, Birmingham, Sheffield, Bristol and Edinburgh, in repeated actions.
“Plans are being made to launch the Tyre Extinguishers leaflet in four other languages as interest grows internationally.”
Earlier this week, Sussex Police issued CCTV footage showing two people it wants to trace in connection with tyres being deflated in Brighton.
Marion Walker, a spokeswoman for the Tyre Extinguishers, said: “Unless a bobby is posted beside every SUV in the country 24 hours a day, we don’t expect anyone to be apprehended.
“Better to break the law than allow these killer vehicles to continue to be used on our streets.”