But, of course, if one were to say pound sign/symbol in the UK, it would be understood to refer to this: £. Now, if Americans needed to refer to £, they would probably say the pound sign or the pound symbol or That little squiggly thing that looks like a capital L in cursive* with a line through the middle. But since they rarely have to refer to £, they're not too bothered by the ambiguity.
The usual UK term for # is hash sign (or hash symbol), but it doesn't seem to have a long history. The OED says:
hash sign [cf. hash-mark: prob. ult. f. HATCH v.2, altered by popular etymology], the symbol #, esp. used before a numeral (as in N. Amer.) to indicate a following number; the ‘number sign’
1984 Which Micro? Dec. 12/2 Neither user-defined characters, nor the ‘*hash’ sign could be reproduced. 1986 Guardian 20 Feb. 15 Would I please therefore oblige her by using the musical notation provided (I gather that it is called a hash sign).The (AmE) quotation marks/(BrE) inverted commas and uncertainty about the term in the quotations suggests that hash sign was only becoming established in English (British or otherwise?) in the 1980s. The hatch mentioned in the etymology is the verb sense of 'To cut, engrave, or draw a series of lines', but although one also sees hatch mark in the wild, there's no indication in the OED that this term has ever been popular. Of course, hash sign/symbol is not restricted to the UK, and its use in the Twitterverse term hashtag will probably give hash an advantage over pound and number in some quarters. Another term that some seem to use is the descriptive crosshatch symbol--though the OED doesn't yet include it.
I can only guess that the apparent absence long-standing name for # in BrE is due to a lack of need for it. BrE speakers weren't using # to mean 'number' or 'pound', so it was only when (AmE, orig. proprietary name) touch-tone/(BrE) push-button telephones became widely available that they had much need for a word for that symbol. (And maybe even later--it was years after we had such phones that we got automated interactions with instructions like "press the pound/hash key twice".)
Because American keyboards typically do not have the £ symbol, people sometimes use # to signify amounts in sterling. My understanding of this has been that it's called the pound sign/symbol because it is used to mean the same as lb. --i.e. pounds as an imperial measurement of weight--then because it was already called the pound sign, it fell into use for the other kind of pound when need(s) be. But Mark Liberman on Language Log has been doubting this, and so my reason for choosing tonight to blog about this is just that it's a good excuse to link to his post.
Oh, and if you don't like any of these, you can always call it an (orig. AmE) octothorp(e), which seems to have been invented in the early 1970s specifically for the phone button.
* While cursive is not marked as AmE in the OED (it certainly wasn't coined in America), it's rarely heard in the UK, where people instead tend to say (BrE) joined-up writing.