Yes that seems sensible, I'll give it a go, though I think it may be more difficult than all sand to fill those holes.
Hi, Thank you for your help with this. Lawn is now aerated using hollow tine tool.
As explained earlier, no cores came out, just pushed soil in.
I used mixture of compost and sand as recommend and it worked fine.
The job was very hard as you predicted, but I hope the lawn will be better for it.
I am waiting for the grass to dry so I can put fertilizer on (complete 4 in one).
I have bought a roller aerator with spike. It looks good and I hope to use it every week or so.
Well done, I'm glad it worked out! No, you won't have to do it every week, thank goodness. Autumn and Spring are the key times, and you will be able to do a really good job with your roller.