Hi there Paul,
Any major currency accepted by the bank money changers. Best to use your home currency as it saves yet another bank charge. Most moneychangers in Phuket don't make a % commission charge and the rate they show is what you get without any other charges.
I don't recommend anyone to carry a large amount of cash, better with traveller's cheques or the cheapest/easiest/most secure way is to use the ATM's with a suitable home cash card.... Cirrus, Plus, Visa, Mastercard. Cheque with your home bank if you are not sure.
Have a good holiday,
Wallee & Alex in Patong, Phuket