In the OS 1:25000 map below I have circled some numbers next to roads. The key says "Ground survey height" and there is another entry (in brown) for "Air survey height", but since all the data in the map comes from a survey of one kind or another, I'm not really sure why this is relevant. You can already tell the height within 5m from the contours, and you can make a reasonable estimate if you want more precision than 5m.

I have tried to think what they might used be for, perhaps for knowing drainage directions, but it seems too little information for that (i.e. you'd need a more detailed and specialized map for that). So...

What are these specific heights used for (why do they appear on this type of map)?

Is there any reason those particular points are used, they seem fairly arbitrary?

annotated map

Above map is © Crown copyright (2016) Ordnance Survey. Used for private research in accordance with the principles of fair dealing as set out in the Copyright, Designs and Patents Act 1988.

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    You have just displayed some copyright material without the appropriate acknowledgement to OS! I recommend you delete this question quickly or acknowledge OS using the method you agreed to in the license... – Hornbydd Feb 21 '16 at 19:44
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    @Hornbydd thanks for the tip - does that look ok? – jhabbott Feb 21 '16 at 22:04
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    I reckon that should cover you, don't want to upset the OS, they do a great job. – Hornbydd Feb 21 '16 at 23:42

The answer is quite simple:

"Spot heights – shown as a number beside a dot – appear at strategic points, including along roads where they level out at the top or foot of a hill. These can be a useful guide where there aren't many contour height numbers."

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    To compliment this answer a trawl of the OS website threw up a definition of Air Height - "A spot height supplied by photogrammetry" – Hornbydd Feb 21 '16 at 23:55

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