I think it depends on a lot of different things...
Firstly there the question of what sort of percentage £20K is: obviously a £20K drop on a house priced at £100K is more of a hit than £20k on a house priced at (for example) £300k.
Then there's the question of how much pressure you're under: if you've found a house you want to buy, there's a risk you might lose it to someone else if you wait for a higher offer.
Then there's the question of how healthy your local property market is. House prices round here seem to have fallen over the past year, and it's not at all clear whether they're going to continue falling, level out, or rise a bit. Unless your local market is healthy, if you wait, you might find yourself getting even lower offers in 6 months time.
Then there's the question of what you have valued yourself against. I'm looking at a house that has also dropped its asking price, but not by enough I think. I know the vendor is comparing himself with other houses nearby that sold last year for £20-25K more than his asking price, and he is thinking £20-25k is a reasonable discount for the work that needs doing. But I think he is under-estimating costs and over-estimating value, partly because he's a DIYer so isn't thinking about what it would cost to pay people to do the work, and partly because he isn't factoring in the fall in prices since those other houses sold, and partly because he thinks his house is in a better state than it actually is. It's hard to be objective about your own house I think.
In my case, I've worked out what would need doing to bring this house up to the standards of the last couple of similar houses that sold on the same street, and it adds up to £21K - so the £10k 'discount' simply isn't enough. If I make an offer, it'll be based on estimates of the work needed to bring it up to the standard of similar houses that have actually sold, rather than to asking prices.