IO540
Sorry to be a bit of a bore. I doubt any part of Scotland surveyed by the OS is miles out. The OS has very, very high standards.
Basic survey involves astronomical observations to stars for position determination and bearings. For this, as you correctly state, time is essential, fundamental even (as it is with GPS, but the world has moved on and accurate time is relatively easy these days). Baselines are measured using calibrated rods - Hounslow Heath was one of the first in the UK - and triangles are observed from one end of the country to the other. Simple trigonometry with big numbers and lots of decimal places. All done before the days of calculators, let alone computers. All rechecked and recomputed since.
In flat lands this is a major pain, often temporary double towers are erected. An internal tower for the theodolite which measures the angle and an external tower for the surveyor to do his observations. By the time the surveyors got to Scotland they were laughing because there were hills everywhere...well apart form the weather, midges and the natives.
Using GPS it is possible to reposition previously coordinated points by Long Range Interferometry. Simultaneous observations are taken at locations hundreds of miles apart. Discrepancies (a survey word for errors) are resolved and a best fit is computed using rigorous mathematical techniques.
Looking at the link identified by Sallyann1234 the whole OS network has moved on in the last few years.
So to get back to the point of this thread..the height on the plaque could be accurate but I suspect not. If you use Sallyann1234's link then you will find a more precise height location to check your GPS against. If your GPS has EGNOS capability (and it is enabled) then you should get a more accurate comparison. If you look on the EGNOS website then it will give you an expected accuracy that you could achieve. The website will probably be quite conservative, in reality you will get better results.