I've come across many references to charity shops in the USA (where they seem to be known as 'goodwill stores' or 'thrift shops'). However, I can't recall seeing any in Paris, Brussels, Genoa, Barcelona, etc. (Although, to be fair, visitors to the main tourist areas of London wouldn't find many charity shops, either).
I suspect that the success of charity shops in the UK is largely due to the fact that they only pay, at the most, 20% of the normal business rates for the property. (In some circumstances, charity shops can get additional relief, reducing their business rates bill even more). If charities, in other countries, have to pay the full rates of local and national taxation, it might be uneconomic for them to run shops similar to those in the UK.
Chris