The park is home to around 500 deer.
"The helmet definitely saved me," Mr O'Reilly added.
"Apart from that, my shoulder was a bit sore and I had a headache."
The competitor completed the race in two hours 25 mins.
Mr Scraggs said he never thought deer would "try and leap over the cyclists".
"I had a feeling they might make their way across the cyclists' path, so I tracked them though my lens," he said.
"I never envisaged that they would actually try and leap over the cyclists. It all happened so fast, It was a really heavy crash.
"It was a relief to see the competitor get back to his feet and continue."
It is understood the deer has also recovered.