As DS is 5 in July it will definitely be Year 1 that he joins in September (reception class if you come back before September)
I cannot help with areas that aren't full really - we're in London and that's the worst place for shortages (also Manchester, Bristol and other large cities can be bad) but that's not to say you wouldn't get into a good school. It is just down to luck with Year 1 places in busy areas - if someone leaves they create a space and in London especially lots of people move every year.
Don't get bogged down by the school thing. As has been said on other threads, find job/jobs first and locate for those. LAs have to find you a school place "within a reasonable distance", if that is over 2 miles they have to provide transport at your DSs age too.
Most primary schools are pretty good (regardless of OFSTED or newspapers). So I wouldn't really panic. Big cities including London often have the most mobile population so even if the school is full it is more likely to have spaces coming up.
You can also move your child if the first school does not work out, and without "wrecking" your child's life.