Network Rail have agreement in principle from Cherwell for the closures. It seems they are not content to wait for the Local Plan to be actioned. On 3rd August, Network Rail wrote to residents (aka some selected "neighbours") saying that it is looking to close both level crossings. You can download a copy of the community letter here.
.... and listed all the advantages
Safer for the public to cross the railway
They also provided a map of the proposed works which is reproduced below.
Network Rail were forced to cancel a planned public meeting in Yarnton due to COVID19 restrictions. We understand it is currently considering how to engage safely with the public.