Ian,
There is a lot of info about the visa situation at:
http://www.usembassy.org.uk/cons_web/faqs/niv/faq_visas.htm#two
I copied the following which I think means you will need a new visa but I would check with the embassy if you're unsure.
"How long is a visa good for?
You may use your visa to travel to the United States until the date it expires, or if your visa says that it is valid "indefinitely", you may use it for ten years from the date of issuance.
I have a visa in my old passport. Can I just transfer it over?
It is not possible to transfer a visa from one passport to another without making a new visa application. Please note that the Embassy no longer issues visas valid "indefinitely". If you are issued a new visa it will have a maximum validity of ten years.
My passport containing a valid visa has expired. I've obtained a new passport; do I need a new visa?
If the passport in which your visa has been endorsed has expired, the visa in the old passport still can be used, provided that you also carry a valid passport of the same nationality. Note: If, when canceling your old passport, the passport authority has clipped the corners of the passport, and, in so doing, has damaged the visa in any way, that visa is no longer valid and cannot be used for travel to the United States.
My old visa says "Indefinite"; is it still valid?
Since February 1, 1995, "indefinite" validity visas have been valid for a maximum of ten years from the date of issuance. Consequently, if the visa in your passport is a B-1/B-2 visa valid for multiple applications "indefinitely" you may continue to use it for business and/or pleasure purposes for ten years from the date of issuance.
The United States Government no longer issues "indefinite" validity visas. The maximum validity of a B-1/B-2 visa is ten years. The ten year validity period applies regardless of the fact that the applicant may have previously held an "indefinite" visa."
Angela