Relatives of two of the four members of the Royal Household Cavalry who died in the 1982 blast said that they wanted “justice” for their loved ones.
Convicted IRA member John Downey was charged four years ago with the murders, which he denied, but the prosecution at the Old Bailey collapsed in 2014.
The case against the Co Donegal man was ended because government officials mistakenly sent him a letter in 2007, as part of a controversial On The Runs (OTRs) scheme, telling him he was no longer a wanted man.
Hyde Park bombing soldiers’ families 'prosecuting ex-suspect'
We just want to get justice for them, no matter how long that takes
Now Sarahjane Young, the daughter of Lance Corporal Jeffrey Young, who was 19 when he was killed, has filed a civil claim at London's High Court against Mr Downey.
The car bomb left in South Carriage Drive killed Squadron Quartermaster Corporal Roy Bright, 36, Lieutenant Dennis Daly, 23, Trooper Simon Tipper, 19, and Lance Corporal Young and injured others as they rode through Hyde Park to the changing of the guard.
Seven horses were also killed as the soldiers travelled from their barracks to Buckingham Palace. Another horse, Sefton, survived terrible injuries.
Relatives of two members of the Royal Household Cavalry who died want 'justice'
Convicted IRA member John Downey was charged four years ago with the murders
Get Quotes on Home Insurance
Backing the claim Mark Tipper, an older brother of Trooper Simon Tipper, said: “If we can get this man before the courts in some way, it will show the British public at least still believes in justice.
“We've been let down again and again by the authorities over the past 35 years and, if I'm honest, at times we've almost given up hope.
“We just want to get justice for them, no matter how long that takes.”
The newspaper is campaigning for people to donate money to fund the lawsuit.