Can't identify it from just the top half I'm afraid, as the bottom halves vary from tap to tap as well. You'll have to take it out, and even then the chances of being able to ID it from photos are virtually nil.
Your best bet is to take it, and the head that goes on it, around all the plumbers merchants in your area until you happen to strike lucky with a matching one they've got kicking around under the counter in a box of random CD inserts they keep for just such occasions. In my experience the independents are better at this than the big nationals, but either way it's going to be like trying to find a needle in a haystack without knowing the make or model of the tap. It *might* help to take a photograph of the entire tap with you (printed out, not on your phone...) in the hope that one of them recognises it. You could even take the photo to Bathstore to see if they know what it is, but I wouldn't count on it, this is rather the problem with buying from this kind of establishment, the backup is often quite poor when things wear out.
If all the above fails it's new tap time I'm afraid, unless you convert it to run off old-style washers which can sometimes be done, but probably not with the heads you have now.