I think it is cheaper in London than HK because I bought a Chanel tote for my cousin several years ago in London and the prices for that bag in HK was around $2000HKD more expensive at that time. If you are a visitor in London, you can get around 10% tax refund. At Heathrow airport, you can get 15% because there is no adminstration charge, this will apply for any passengers at Heathrow (EU residents or visitors). However, I think you can only find Chanel store at Heathrow Terminal 3, there are 4 terminals in total. Although it is cheaper to buy Chanel at Heathrow than in other Chanel stores in London, you will have to take the risk if that item you want is not in stock in Heathrow.
Final point, because the exchange rate for Pounds is so strong now, I am not 100% guarantee that Chanel is cheaper than HK. Any chance that you will go to Paris, may be for a day? It only take 3 hrs on Eurostar from Central London to Central Paris. Chanel in Paris is around 10% cheaper than UK. Hope this helps.