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Two chairs like that must be worth at least a thousand pounds up in London.

I don't know what the 'up' mean in the sentence. I'm even not sure which words — perhaps either 'a thousand pounds' or 'in London' — are modified by it.

"Up" and "down" have meanings that refer to towns, cities, and other possible destinations.

Compare this meaning and example sentence for "up" in the Oxford Learners' Dictionary:

(adverb) 1. towards or in a higher position

They live up in the mountains.

The mountains are in a higher position. It'd be possible to just say "they live in the mountains," but the "up" gives an idea of relative position - they live up in the mountains compared to where the speaker is talking. (The valley? The plains? Anywhere else lower?)

What gets tricky is what precisely "higher position" is referring to. Is it elevation? Latitude? Political or economic prestige? For the last value (prestige) there is a specific meaning for "up":

(adverb) 4. to or at an important place, especially a large city

We're going up to New York for the day.

New York is down in elevation and latitude from Rochester, but someone from Rochester may well go "up to New York."

This adverb up commonly comes before prepositions like "up to," "up in," and "up at." "Down" has a contrasting meaning, and different locales or individuals may have their own idea of whether a city qualifies as "up" or "down" relative to them. (One can use both "down in London" and "up in London.")

I (born 1964) was brought up south of London so I have personal experience of this problem. We always went up to London. As there was no obvious altitude difference, I always assumed it meant "up north" but my dad (born 1916) assured me that London was always up. He was brought up north-west of London. He further told me that it was a rigid convention on the railways (and we would always have travelled by train) that the up train went to London and the down train came back.

The Free Dictionary supports this claim that there are two different definitions in use, and this document from the the Indian Railway Fan Club (see section on "Up and Down Trains") says

Down refers to a train travelling away from its headquarters (i.e., the homing railway) or from its Divisional headquarters, whichever is closer. Up refers to a train travelling towards its headquarters or divisional HQ, whichever is closer. [...]

History

In the UK, the convention was that all trains going to London were "up", and all those going away from it were "down".

I am pretty certain (from experience) that my dad was right, but equally certain that it is not common practice these days. It may well depend on direction - you might be more likely to go up to London if it were east than if it were south. I would definitely go down to London these days from where I am now in Scotland.

In short, I am sure up is definitely the direction of London, but we cannot be sure, without further context (i.e. date and location) if it meant "up north(ish)" or "towards the metropolis".

In this example, the implication is clearly that prices will be higher in London than where they are now.