Typically the only time there is an accepted "equal to " situation if a material is dual certified and this allowance is spelled out.

But then again the specific quoted British Spec is not known to me.

There are quite a number of "equivalence tables" on the current literature (books, catalogs etc.) showing the "equivalent materials" covered by different standards :ASTM, DIN, BS, AFNOR (French), JIS (Japanese) etc. etc.
These tables are indeed very useful, but they must be handled with care. What they actually show (no matter what they claim they are) IS NOT that a certain ASTM material is EQUIVALENT to such and such DIN one, but that those two materials are just SIMILAR in their properties and may be used for similar applications, provided that you use the properties applicable to the material you selected in the table, not the original one.
Let's give an example. Suppose you are in Germany and you must design a steel structure. Being familiar with American standards, you decide that ASTM A-36 would be the correct steel to use, if it was available in Germany. As it is not, you look into a table and see that the "equivalent" German material is DIN St 37, which you decide to use. Attention though!! When making your calculations, you MUST NOT use the A-36 allowable tensile strength but the St 37 allowable tensile strength. Understand what I mean?
With this in mind, you can look at any of those tables I mentioned and find by yourself which is the material you're looking for.
A word of caution: all the tables I know show ASTM materials; I've never seen ASME being cited. However, as the great majority of ASME materials are identical with ASTM, I believe you won't have any problem.
Giovanni S. Crisi
Sao Paulo - Brazil