"Come to our bash - and give us some cash!" 
I suppose you could always have a Bank of England wedding list, so when people think "Hmm, we want to spend about £40 - is there something on the list to that value?", they can look and see "Ah, yes - '£20 Note - qty requested: unlimited' - we'll get them two of those" 
I can't speak personally for South Asian cultures, but in traditional British culture, I think the idea that the couple asking for money that they probably need and can always use rather than one of 17 toasters (when they already had one anyway) is rude is probably one of those things like 'no elbows on the table' - it's 'rude' because 'it's rude', but when you stop to ask why it's rude.... nothing.
Even with gift lists, it still restricts you to one shop and having to base your choice of requested gifts on what John Lewis sells rather than your own best choice. As PP said, it also avoids the issue of necessitating a certain-value compartmentalised gift from each guest/couple/family when what you really want/need is far more than any individual guest would/could give.
I think, as long as it's done tactfully (which 'no boxed gifts, please' seems to do well), I really can't see why not.
This reminds me of a Weddings thread from some time ago, which featured some absolute gems, such as the couple who asked for cash and then emailed people afterwards if they didn't believe their gift was commensurate with their perceived means and inviting them to 'do the right thing' by topping it up (I don't know if they similarly contacted the over-generous poor guests to insist they take some back); and the couple who had a feature wishing well for money gifts, but instead of emptying it at the end of the evening and being grateful for all they received, the bride stood there throughout and immediately emptied out any gifts that were put in the well, whilst the giver was still there, to check if the person had given 'enough' 