The new Oldton school must have been a private school. How else could it afford to have such large playing fields?
It may well have been called Lambertes School at some point, as there is some evidence that the Lamberte family crest was used as the school badge.
The photo of the school in my possession shows a dense collection of modern buildings, suggesting that Oldton didn't disappear until quite recently. But a photo of an Oldton church kneeler shows a much older building (presumably on the other side of the school grounds) and a date of 1969 is given for its demise. I was five years old in 1969.