Musicians object to political song use

The IPKat notes a letter in today's Times from the Musicians' Union and the Features Artists' Coalition, protesting at the use of songs by the their members on a compilation put together by the British National Party.

They note that many of their members 'have no legal right to object to their music being used in this way' and add that:
'we would also like to raise awareness of the terribly low level of moral rights accorded to musicians in this country and we call for these to be reassessed so that musicians are able to object to their music being used in situations which contravene their beliefs and morals'.
The IPKat can see the correspondents' point of view. If one can object to one's trade mark being used in an unsavoury context, then why not one's literary, musical or artistic work or one's performance, which if anything, is more personal to the author than a trade mark is to the company that it represents. The Kat seems to remember the Musicians' Union raising just this concern at the time that performers' moral rights were brought into force in the UK. The IPKat is somewhat puzzled though. Can the performers not rely on their economic rights? If they've dispensed with them, can they not persuade their labels to take action? Aside from the political ramifications, sure they record labels and the authors of the underlying copyright works don't want the BNP making use of their copyright-protected works for free.