"Firstly, as people have said, see why the school 'requires improvement'."
Absolutely. Read the text of the report BUT I would start from the assumption that no school in a 'good' area should be in that category. Essesntially, in a 'good' area, a school will tend to have many things going for it - a low level of deprivation, a reasonably high level of parental education and support for school, the ability to generate extra money through a PTA etc, relatively few social problems, etc etc.
Obviously looks can be deceiving - locally, an area of town LOOKS very properous, but in fact the big mansions are divided up into flats and bedsits, and the poor reptation of the secondary drives educaionally-savvy parents out. the few familuies who do live in 'undivided' large houses go private.
But in general, a scjhool in a good area will have to 'work less hard to achieve the same results'. To require improvement in such an area, a school may be coasting (relying on intake to get good results), may have had a rogue poor year, may have failed to move with the times, may have gone through a period without a head, may have one or two poor or time-served teachers ... some of which are rectifiable in a very short time, but others of which take a real effort to turn round.
Read the report in detail, read the school's response to it (defensive tone is BAD, run a mile), go in and ask really detailed questions about how they have responded (ask for evidence).
The ONLY excepton is, I would say, if your child is unusually sensitive or exceptionally (and I mean exceptionally, not MN normal) able. In that case, you might select a school based on peer group, even if you know that the school itself isn't as good in terms of enabling children to make good progress. In a school in a very deprived area, there will tend to - there are obvuiously exceptions - be a slightly smaller percentage of highly able children, and thus an exceptionally able child may not have a peer group, especially if the school is small.