Can you recommend a fertiliser for a lawn on (London) clay soil that's not doing very well :(

[AlienShmalien]

Just that really, our lawn has never done very well.
I've tried spiking it but no big improvement resulted.
It has to be pet friendly as we have a cat.
Thanks in advance.

Put sand on it and rake it in, and if it's still waterlogged after that, you'll need to dig a French drain.
That's a long trench at the lowest edge of the lawn, with a layer of gravel at the bottom , then a pipe with holes drilled along it, then fill in the trench. Water will always drain to the lowest point.
If the soil is badly drained, no amount of Fertilizer will fix it.

Thanks. I do actually have a french drain, pretty much as you described (though I didn't put it in for the benefit of the lawn).
I don't think it's waterlogged or anything like that but the clay becomes very compact.

Anyone have any fertiliser recommendations?