Doesn't look so bad to me. It does need to be mowed.
Since we have to assume you're in the UK, it's early
Fall now. You could overseed it, but from the pics, not
sure it's warranted. If you do that, I'd rent a slice
seeder, which I would think is available in the UK.
That cuts slits and drops seed. This scarification
stuff I believe is what we would call dethatchiing in
the US. It's hard on the lawn, will damage more of
the existing grass and is only appropriate in you have
a thatch problem.
Otherwise I would apply a regular fertilizer now and
then a Fall fertilizer a month later.