1)Why are prices generally usually higher for goods or services in London as opposed to Newcastle, or New York as opposed to San Fran?

I understand that inflation is caused by excess demand/liquidity which causes the price of inputs such as raw materials to rise. But is the answer to the above question attributable to this fact. I don't feel it is because prices tend to rise higher in London as opposed to Newcastle as well. I felt that it is because the market can bear a higher price (taking into account competitive pressures) and the london economy can still grow because a great deal more money flows into it. To me this increased demand does not affect the price of inputs but does enable firms to charge a higher premium - is this true?

2) If it is , then is there any difference at all between the kind of inflation thats pushes input prices up and the kind that allows firms to chrge higher prices because there is a higher demand in that part of the country? - because they both end up with the same result .i.e higher prices.

3) by extension of logic , if a firm can (taking into account competitive pressures)charge a higher price in newcastle because of higher demand then will it - but this will have no impact on the price of inputs right?