Aerate and overseed or rotate? (UK)

Had a thick lawn last year that overall was in good shape. We’ve since had some work done and the lawn has been trodden all over.

Now I’m sure the grass roots are likely intact and with an overseed and a feed it will come back perfectly fine. But it’s also fairly compacted.

So rotavate and reseed or just core aerate and overseed?

EDIT: title should say rotavate