Question
Our old laurel oak has suddenly started dropping heavy quantities of sap, which has never happened before.
Is this something that can be treated?

Answer
I am going to assume you are talking about the sap raining down like a mist not pouring down the trunk. IF so this is caused by sucking insects either aphids or scales. These insects suck the plant juices form the plant and secrete a substance called honeydew which is sticky and high in sugar content. Usually a sooty mold will grow on the honeydew and ants will crawl harvesting the sugar.

I would guess this is scale insects. Scale insect look like small turtle shells or bumps on the twigs and small branches. The insect lives under this shell. Control the scales and the sap will stop dropping.
Since this sounds like a large tree I would use an insecticide called Bayer Advanced Tree and Shrub Insect Control. This is applied around the tree and the roots will carry it to the leaves and twigs and when the insects suck the plant juices they are killed. With a large tree it will take a week or so for the insecticide to reach the top of the tree. This treatment will last all season long. Here is a web link to this product--check with your local garden type store for it.
http://www.bayeradvanced.com/tree-shrub-care/products/12-month-tree-shrub-insect...
The tree could be sprayed BUT it would take a power sprayer to reach the top of large trees and you would need to coat the foliage and twigs good. The soil applied is much easier.