We moved house last year, and I've noticed the lawn is in quite bad
condition.
To start with, there are numerous pot-holes and uneven patches which
can be noticed as you walk on the grass, some of which could turn your
ankle. This makes it impossible to cut the grass down to a fairly short
level as my rotary mower just grounds itself and can't be pushed.
Secondly, the grass has a 'spongy' feel when walked upon. Could this be
due to a build up of thatch? There are patches where I can see a lot of
clover and other weeds, but very little grass.
Thirdly, I know the soil is heavy clay based, and there are also
numerous trees surrounding the garden. Could this be causing drainage
problems?

I'm just looking for advice on the best way forward to improve the
quality of the lawn. If this means ripping up the grass and re-seeding
or turfing, then fair enough, but is there anything I can do in the
short term that might improve the situation?

Thanks.