Soggy lawn

Hi, hoping someone can give me some advice as I haven't a clue.
A few years ago we decided to level the lawn, in doing so we removed a lot of the topsoil. Since then the lawn in parts becomes a muddy mess after raining.

So was wondering if I ordered some topsoil could i just put it on top of the existing grass or would I have to dig it all up. I'm not looking for a perfect lawn just one that is usable for the kids.
I wouldn't be putting drains in either, just trying to rectify our mistakes on a budget!
Any advice appreciated Thanks.

If u join garden.ie with gerry daly he gives advice. Personally i wouldnt go do any lawn work till the rain spell is fully over as it would be very mucky at moment.

I put about 6 inch of stones under our lawn and drain tubes, a lot of hard work but worth it.

Thanks I'll try garden.ie. Don't want to go down the route of installing drains so I'll see what advice I get on the other site.
Thanks again to you both.