Ten people died when the police helicopter crashed into the roof of the Clutha pub on November 29 last year.
More than 100 people were inside the city-centre bar at the time.
Irwin Mitchell's specialist aviation law team has sent a letter of claim to the legal representatives of Bond Aviation Group and also reiterated calls for a full examination of what can be done to improve flight safety.
One client the law firm is representing in the compensation claim is John McGarrigle. Mr McGarrigle's father, also called John, died when the helicopter crashed through the roof.
It has not yet been established what caused the helicopter to fall from the sky, although investigators say initial evidence rules out engine or gearbox failure.
Irwin Mitchell partner Elaine Russell said: "Our clients have faced a difficult and traumatic time across the Christmas period after losing loved ones in the Clutha tragedy and we continue to eagerly await further information from the Air Accidents Investigation Branch (AAIB) regarding the progress of its investigations.
"However, we have now issued a letter of claim to Bond Aviation Group which, as the owner and operator of the aircraft, is legally liable for the deaths of the police passengers and the ground victims in the pub, as well as those who were injured in the pub, under a legal concept known as strict liability.
"The response from the Glasgow community has been heart-warming and there are many fundraising efforts taking place to help those affected.
"We are absolutely determined to ensure that those who lost relatives in this crash not only get the financial support they may need following the incident, but also the answers they are desperately seeking in relation to the crash."
The legal team has also launched a campaign demanding the installation of vital black-box recording equipment to be standard on all commercial passenger-carrying helicopters.
Air accident investigators have already stated that the helicopter pilot made no mayday call and that no black box data recorder was on board.
Jim Morris, a former RAF pilot and partner in the specialist team, said: "As part of our commitment to achieve justice for our clients, we will do everything we can to ensure that helicopter safety is a priority.
"An important factor in this is the need for review and amendment of helicopter regulations.
"This includes a change in legislation to require all commercial passenger-carrying helicopters to be fitted with flight data recorder (FDR) and cockpit voice recorder (CVR) equipment.
"Too many people have lost their lives or suffered serious injuries as a result of helicopter crashes in the past five years and this simply cannot be allowed to continue any longer."
The helicopter crew of pilot David Traill, Pc Tony Collins and Pc Kirsty Nelis died in the Clutha crash as well as seven customers in the pub.
They were John McGarrigle, Mark O'Prey, Gary Arthur, Colin Gibson, Robert Jenkins, Samuel McGhee and Joe Cusker.