I'm sure that the situation varies a lot according to the nature of the work and the trade/profession concerned. In my world, one of the very first questions one almost invariably gets asked is about one's 'hourly rate', and if someone based in central London quoted a much higher figure than, say, a person based in rural Cornwall or Wales, they simply would not get any work!
If that rate is calculated 'reasonably' that's fair enough. Customers/clients in London will undoubtedly expect and accept a much higher rate than they would in some different places "because that's how it is" - but that doesn't stop me asking whether "that's how it should be", at least in some contexts.
Despite what you and others may think, I am not being awkward or argumentative for argument's sake but, rather, genuinely am interested to know the answer to the "Why?" question - since I suspect that, at least in some cases, the answer may be "because that'show it is"! As I've said, there are certainly situations in which the cost of services, and maybe goods, is justifiably appreciably higher in places like London - particularly when 'premises' are involved, but I'm far less convinced in some other contexts (trades/professions).
The 'total' is obviously the most important bottom-line for a customer/client, but everything depends on how 'reasonably' your (differing) totals were calculated.
If you merely took the 'hourly rate' you would charge for work within walking distance if you lived in, say, rural Wales and added to it a genuine estimate of travelling costs and some reasonable amount of remuneration for 'travelling time' and 'being away from home time', then I think that would be fine, and fair to everyone. However, I suspect that a good few people in that position would charge a higher hourly rate for work in an 'expensive' place (like London), before adding on those legitimate 'addons' - solely because "rates are higher in London".
As a matter of interest, to help my understanding, if you lived in an expensive part of London and worked as a full-time in-house (no travelling) employee at a site within walking distance of your home, would you expect a higher hourly rate of pay than if you were in exactly the same situation, other than living in some very rural part of the UK? Similarly, what if you were self-employed and (largely as is the case for me these days, although not in the past), virtually all of your work was undertaken 'remotely' ('from home') - would you then feel that you should charge appreciably more if you were doing it from your home in central London than if your home were somewhere very rural and 'cheap'?