The project has started Phase III of the human trials to assess how the vaccine works in a large number of people over the age of 18, but has yet to report Phase I trial results.
The developers of the vaccine earlier this month said they are encouraged by the immune response they have seen in trials so far.
"I am hearing there will be positive news soon (perhaps tomorrow) on initial trials of the Oxford Covid-19 vaccine that is backed by AstraZeneca," Peston said in a blog post on Wednesday.