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In London, I suggest you spend a total of 3 days to visit "British Museum"; the "Parliament House"; "Greenwich"; the China Town (i.e. Tube station: Leicester Square); and the Palace (also see the Marble Arch and Trafagular Square). All these places are earily accessible by the Tube (MTR equivalent) and the Bus - BUT do remember to buy an "Oyster" card before you leave the airport (Heathrow) to the Tube station at the British Travel Office. You will find using "Oyster" (like our Octopus Card) much cheaper and easy than paying cash.
I also suggest you spend one day at each of these cities: Bath, Portsmouth, Oxford, and Cambridge. All can be reached from London by Train (very expensive) or by Coach (at Victoria Coach Station). At Bath, you see the Roman Bath. At Oxford and Cambridge, you will see Universities. At Portsmouth, you can see the Marine Museum (and a nice shopping center with factory outlets).
From London (Waterloo station), take EuroStar to Paris. Stay in Paris for 4 -5 days. You can use the Paris MTR to move around. Of course, apart from shopping, you should also visit Eiffel Tower, Louvre, and Versailles Royal Palace (this one by bus).
On returning to London, do some shopping at the Oxford Street and Regent Street. But buy Burberry, Gucci, and Channel inside the Airport to save the trouble of lining up for tax rebate!
Good luck.