Accurate mapping is because of rebellious Scots
1745 was the start of the Jacobite rising in an attempt the claim the English throne. It ended in April 1746 with the battle of Culloden. The English Government of the time feared another rebellion on ground that they just did not know. They also feared attack from the French to the south. The main problem was they just didn't know where to place defences as the maps they had at the time were dreadful. Enter William Roy. Roy was an Engineer. Starting in 1747 and using simple compasses and 50ft long chains, in 8 years Roy created a small scale military map of Scotland. Roy was only 21 when he started. In 1784 he was commissioned to survey the distance and angle from the Royal Observatory in London to the Observatory in Paris. He started by first setting a 5 mile long base line on Hounslow Heath. He completed his survey, but what he really wanted to do was complete a survey of the whole of the UK. Roy died in 1790. The Board of Ordnance started out on this survey in 1791 and the Ordnance Survey was born.
In theory, if you have two known points and want to find the position of a third point then all you have to do is measure the angle between the known points and the unknown point and do a bit of basic trigonometry to give you the co-ordinates of the third point. This is called triangulation. If you extend this across a whole country then you can accurately map it (allowing for a few factors like curvature of the Earth etc).
To accurately measure angles William Roy and his surveyors used (and we still do now) a Theodolite, which have been around since the 16th Century. The maps that the Ordnance Survey made between 1783 and 1853 were okay but after the Great War (1914 - 1918) the UK Government again decided it needed better mapping of the UK. In 1935 Brigadier Martin Hotine was given the task of mapping the UK - creating a National Grid.
However, to take accurate measurements then multiple "sightings" must be made and to the same spot each time. This is where the Trig Pillar come in.
Hotine designed it so that a Theodolite could be strapped accurately to the top of it time and time again. You could also strap a sighting post or Target to the top so that you would be measuring to the same point each time.
Over 6500 of these were built all over the country. The first being at Cold Ashby, Northamptonshire on 18th April 1936.
The trig pillars were all built by hand and the final one was built and the final measurement and calculations taken in 1962. With so many measurements taken and calculations made, a little bit of error did creep in. When the UK was re-surveyed using modern satellite measurements, the UK was found to be ~20m shorter than the original survey implied. However all these measurements were taken by hand and eye and the calculations done in the head and by slide rule. 20m seems pretty accurate to me - I once set out a concrete retaining wall on the wrong side of a road FFS by putting my decimal point in the wrong place.
The surveyors of the Retriangulation survey of the UK in 1936 may not of been as good as George Everest in the Great Trigonometrical Survey of India in 1856 though. Transferring a level from the Bay of Ganges and measuring angles all the way they surveyed the Himalayas. Due to political constraints they could only get to within 108 miles of Chomolungma (The local name for Everest at the time). After measuring it from 6 different locations they calculated the height to be 29,000 ft. This seemed too perfect so they added on 2 ft and reported the mountain to be 29,002 ft.
Today Everest is measured as 29,029 ft and is reportedly growing at 4 mm per year. So that accounts for 2 foot. Therefore George Everest and his team from 108 miles away to a snow capped summit were accurate to within 25 foot. That is accurate work.