I don't claim to be an expert but this is my understanding. There are three areas of coverage required:
1) Your health / repatriation
2) Liability for bending the aircraft
3) 3rd party liability for any other damage you cause
The 1st is best covered with travel insurance, ensuring that you are covered for private flying (most cheap policies do not). Traffords offer policies of this type.
The second and third are covered by renters insurance, which can usually be arranged through the school or FBO. There has been discussion that you need a US address for coverage but teh FBO address should be sufficient. I know of one UK pilot (who will no doubt be along shortly) that has successfuly claimed.
If you are with an instructor then (2) and (3) should be included in the rental rate, but you still need to consider (1).