In article , Chris Green
wrote:

Any and all advice would be very welcome.

rotovator is what you need

I suppose so, we do actually have an old (but functional still) Howard
Bantam. If set to a fairly shallow dig that would do the job (and
develop my biceps!).

Not advice, just a mild suggestion: I bought an Aldi electric scarifier
a few years ago.

It's a fearsome heavy beast, about (?)45cm wide, and has interchangeable
bars - one is blades, one is wire hooks. I tried it out on our tiny lawn
(about 4m wide and 12m long) and it seemed about to rip it to shreds,
even on the highest (i.e. mildest) setting.

So I took it to the place where I do some gardening for the owner, and
the two areas of grass are a lawn twice the size of ours, and a large
sward about the size of half a football pitch. We use the thing
occasionally to rough up the grass.

It occurs to me that if I had your problem, I'd use the "scarifier" to
try and even it out.

My 2p (or 1p, really)

John