My son's lawn has a dip in the middle. The whole area is probably 60 ft
x 20 ft and the centre is about 3" lower than the edges. I thought of
trying a quick fix by leveling with topsoil/sand/seed and hoping the
existing grass will grow through it. Is that a realistic expectation?

I read a long discussion about it on Gardenweb, so I know about sand
types etc, but what works in the southern USA might not be successful in
SE England. With a toddler charging about, doing a proper job isn't an
option for the foreseeable future .

Any advice welcome