Crime statistics in the local area tend to have a large impact. A buyer has the means to check this quite easily, and even if they don't one can generally make a quick assumption about an area one has just visited.
As for amenities, proximity to transport links, shopping and entertainment go hand-in-hand, so it's hard to measure the impact of just one of those. Research suggests that being within half a km of a tube station in London can increase the selling price of a property by about £25K.
Being in the catchment area of a good local school is likely to increase family interest, and will be more important than other aspects (given access to driving) than to young professionals, singles, couples without children etc.
What seems to affect valuations most is the selling price of comparable local properties - which is bound to be lower in a suppressed market. Agents take this, and potential interest, into account more (one might argue) than local features and amenities.
The prevailing affect on selling prices is buyer interest. Resale price of properties that have been sold more than once since 1990 is by far a more accurate indicator of house price movements IMO, which is why I tend to trust the Land Registry's index over others.