This may help you discover where the records are. It looks like they are part of the Dorchester PR's. The originals of those are held in the Oxfordshire County Archives, Cowley, Oxford. The contents have mainly been transcribed by OFHS but as I say above I do not see Burcot within the OFHS index, so you may need to ask them direct if no one offers on here?
Burcot lies on the north bank of the Thames, 1¾ miles north-west of Dorchester. Its historical relationship with Dorchester cannot be precisely defined: for long it has been dependent ecclesiastically on Dorchester (fn. 1) but independent for civil purposes. (fn. 2) In the 18th century it was described as a separate parish, and in the 19th century was placed in a different registration district and rural district from Dorchester. (fn. 3)
In 1932 Burcot civil parish was transferred to Clifton Hampden. (fn. 4) Its area in 1881 was 679 acres, of which 21–6 were detached meadow (Revell Mead) and lay in Clifton Hampden. (fn. 5) The only natural boundary is the River Thames, which has naturally played an important part in the economy.