How would people rate the importance of independent access, and how
would that be reflected in the price you`re willing to pay?

I've lived with both.

The main advantage of rear access is moving dirty garden waste. The second
best thing is being able to move large furniture into back rooms that won't
fit through the house.

However, despite this, I now prefer my current house with no rear access.
The security aspect is very reassuring. Basically, the sort of low life scum
that breaks into houses are usually too lazy to even come to our road,
generally prefering to terrorise their impoverished neighbours. Even if they
did, they certainly wouldn't bother getting their fat McDonalds and crack
laden arses over 3 separate fences just to get into the back of our house.
The front of our house is very visually exposed and right under a bright
street light.

Christian.