Obviously, you have to be certain that the work did not adhere to any formalities and you understand well all the circumstances. I do not believe that what you described would be in the public domain. For sound recordings published outside the US between 1923 and 1989, and that are in the public domain in its home country as of 1 Jan. 1996 or there was US publication within 30 days of the foreign publication they would be subject to state common law protection and enters the public domain on 15 Feb. 2067. I just gleaned this from my chart, but there are a whole host of special circumstances that can matter greatly. Further, this pertains to the sound recording itself and not the underlying texts or compositions.
If you plan on investing in this, you are advised to consult a lawyer in private and have them carefully verify the state of of the material under copyright law.
Most of us here, including myself, offer a free phone consult and I too am in NYC.
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For a 1960 recording you are correct on the UK term being 50 years. http://www.ipo.gov.uk/types/copy/c-duration/c-duration-faq/c-duration-faq-lasts.htm On 2011-09-27 the EU parliament extended protection to 70 years and added a number of other provisions. http://ec.europa.eu/internal_market/copyright/term-protection/index_en.htm and runs that protection from publication rather than from the author's death as in the US.
Go to the following website and use the "tree-view chart" to calculate the term by scrolling down to "Foreign Works" and going through the online interview by clicking on the plus signs and answering the questions.
http://chart.copyrightdata.com/#top You will get an answer tailored to your fact pattern.
A key missing fact is whether the song was published in the US within 30 days of being published in the UK. Assuming it was, then it's necessary to know if there was a US copyright registration. If yes, then the US Copyright remains valid if it would otherwise be valid.
Or, for a definitive answer, see one of the copyright attorneys here on Avvo to do that for you.
I am not your lawyer and you are not my client. Free advice here is without recourse and any reliance thereupon is at your sole risk. This is done without compensation as a free public service. I am licensed in IL, MO, TX and I am a Reg. Pat. Atty. so advice in any other jurisdiction is strictly general advice and should be confirmed with an attorney licensed in that jurisdiction.
Asker: Your question contains a basic mistake. The European Union extended copyright protection from 50 to 70 years, and therefore, a 1960 UK recording is not in the public domain in the European Union (which includes the UK). Further, in Europe there are moral rights for authors of works even after statutory copyright protection expires. The US copyright status of a sound recording like this involves a tangle of rules but you should not assume it is in the public domain in the U.S. It probably is not. Further, the US and the UK are members of the Berne convention in which member states respect each other's copyrights. Therefore, I would start with the presumption that this sound recording remains protected worldwide until proven otherwise. You need to work with copyright counsel on this. These things can be more complicated than you may believe.