Jockey Freddy Tylicki remained in a "stable condition" on Wednesday after the four-horse pile-up that also involved champion jockey Jim Crowley.
Crowley suffered a broken nose in the incident at Kempton on Monday.
The Injured Jockeys' Fund said there may be an update on the condition of Tylicki, who has been in intensive care, later in the week.
Crowley's agent, Tony Hind, said it was "a massive relief" the champion's injuries had not been more serious.
Hind added: "He feels like he's had six rounds in the ring with Anthony Joshua at the moment."
The pair were injured in the 15:20 GMT race on Monday and taken to St George's Hospital in Tooting.
Jockeys Steve Drowne and Ted Durcan were also unseated in the incident.
They were thrown from their mounts on the turn into the home straight but walked back to the weighing room and were checked out by medical staff.
Durcan said he took himself to Cambridge's Addenbrookes Hospital.
"I fractured my right ankle, but it could have been a lot worse," he said.
"I don't know how long I'll be out, but it's not the end of the world and I just hope Freddy is OK."
The incident happened in the third race, the maiden fillies' stakes, as the field rounded the home turn.
Tylicki suffered a heavy fall on Nellie Dean after appearing to clip heels with leader and eventual winner Madame Butterfly.
Crowley and Electrify were racing immediately behind and were brought down, as was Drowne's mount Skara Mae. Durcan was also caught up in the melee and was unseated from Sovrano Dolce.
The horses involved were not reported to be seriously injured.