Ms Sabben-Clare and passers-by, including a vet, attempted to prise the dog off the wild animal, which was later taken to the South Essex Wildlife Hospital in Tilbury.
The seal was treated for a broken bone, a dislocated flipper and joint, ligament and nerve damage.
Warning: Graphic image below
The death of the seal, which gained its nickname through its playful antics on the riverbank, has led to new demands for dog owners to exercise better control of their pets.
Ms Sabben-Clare, 49, whose father James was the headmaster of top public school Winchester College, said: “I am heartbroken by this terrible accident.
“As an animal lover, I fully understand the dismay that has been expressed. I apologise unreservedly for what happened. In hindsight I wish, of course, that the dog had been on a lead but at the time that did not seem necessary.
“I am hugely grateful to all those who helped at the scene. They were heroic. I left for my own safety and that of my dog, believing that there was nothing that I could do to help as the seal was being looked after by a vet and help had been called. I offered my contact details to the vet before leaving.”
However, the QC – educated at Winchester College and New College Oxford before being called to the bar in 1993 – insisted she had repeatedly tried to contact officers.
The barrister, a member of 7 King’s Bench Walk chambers, said in her statement: ”Early yesterday morning I contacted the police to speak to them about the incident and was directed to the RSPCA.
“The RSPCA interviewed me and confirmed that they were happy that no offence had been committed. I tried to contact the police again repeatedly yesterday afternoon, in response to a statement from them that they wished to identify me and speak to me. They have still not been in contact.
“I have made a donation to the Wildlife Hospital which treated the seal. What wonderful work it does.”
The law does not require dogs to be on leads in open spaces but it is illegal for them to be “dangerously out of control” anywhere, with potential penalties of up to six months in jail or an unlimited fine.
The death of the seal was met with dismay among residents of west London. Sir Craig Oliver, former director of politics and communications for David Cameron, said: “So sad to hear that the beautiful seal that took up residence near Hammersmith Bridge had to be put down after being savaged by a dog.”
One of the witnesses to Sunday’s attack was photographer Duncan Phillips who was shooting images of it when the incident happened.
He told MyLondon website: “It was quite a vicious attack. The dog just wouldn’t let go despite repeated attempts by members of the public to separate the animals.”
Police said they are investigating the incident.
A spokesman said they are looking to identify witnesses and will speak to the owner of the dog.