It is common knowledge that London prices are much higher than that of the rest of the UK. However, I have heard that this isn't strictly true; the prices of most typical purchases from food and drink, going to the cinema, through to buying a new TV are much the same as elsewhere. Often quoted average London prices are the result of there being more high-end establishments, skewing the mean, but not actually raising cost for the typical shopper. There are a few things which blatantly cost more than elsewhere, such as the the cost of housing, but the idea is that this is the exception not the rule.
Anecdotally I've found this to indeed be the case. I've been to London a number of times and haven't noticed paying more in restaurants, pubs or supermarkets than elsewhere. As such I've assumed the above to be true and stated it as such to a friend at the weekend. However, it occurs to me that I may be entirely wrong in this as I only have evidence which is either anecdotal or that I've heard at some point from some forgotten source. I have tried to find some more concrete evidence one way or the other but haven't found much other that the previously mentioned "average" prices which do not note whether the average they refer to is the mean or the median price.
I am therefore wondering: are median London prices actually higher than that of the rest of the UK, or are there simply more high end establishments skewing the mean?
To help demonstrate my line of thinking, here are some examples. Would I pay more in London than the rest of the UK for: a weekly shop at a Sainsbury's? A pint of Peroni at an equal-quality pub? A steak at an equal-quality family restaurant? A movie ticket at the Vue cinema?