Quite simpy, if you receive a supply at HV, and under certain other conditions according to ESQCR if you take a supply at LV, you will have a connection agreement that tells you what you should expect at the supply terminals, which will not necessarily be U₀ + 10 % / - 6 % for a "standard" LV public supply.

There's no way that BS 7671 could know what terms you have agreed with the supplier ... and therefore the standard can't be specific about this.

Just a thought here. Is there any provision which specifies voltage drop at HV. Surely, if HV is low, Lv must also be low?

I trust what you are saying is correct, but not following how this is applicable to the question. 

What I'm trying to understand is how the designer of the installation specify the volt drop in terms of BS7671, when faced with the above scenarios? Assuming he has no knowledge of ESQCR.

Assuming he has no knowledge of ESQCR.

The ESQCR should be freely available public knowledge -

https://www.legislation.gov.uk/uksi/2002/2665/contents/made

(including subsequent amendments:

https://www.legislation.gov.uk/uksi/2006/1521/contents/made

https://www.legislation.gov.uk/uksi/2009/639/contents/made

)

   - Andy.

Assuming he has no knowledge of ESQCR.

The ESQCR should be freely available public knowledge -

https://www.legislation.gov.uk/uksi/2002/2665/contents/made

(including subsequent amendments:

https://www.legislation.gov.uk/uksi/2006/1521/contents/made

https://www.legislation.gov.uk/uksi/2009/639/contents/made

)

   - Andy.