Cavendish and Country helped me with my recent house move, and they were excellent. I understand they are capable of helping with international moves as well. Would definitely recommend you give them a call, the number is 020 7733 5577.
I can recommend Santa Fe, we used them for an international move recently. Do make sure you shop around though to find which company suits your needs best -we got 4 quotes from different companies and found cost/transit times/insurance details etc varied a great amount!