Dead patches on lawn

[herbivore]

My lawn is roughly 140/150 sq. metres and up to this year was in reasonable condition.

Now after this heatwave I have many areas of dead grass. Normally after ordinary drought and subsequent rain it begins to recover. However this years intense heat has killed lots of grass. Please don't tell me it WILL recover as I am convinced it will not.

I an wondering what to do. I think scarifying might be a starting point but should I delay this to a bit later -say Sept/Oct?
I feel if I scarify now I will only have exposed soil on which only weeds will grow.

So after scarifying would I be best advised to sow grass seed and if so when ? is spring the best time for grass to germinate?

In the past I gave used Aftercut fertiliser and had satisfactory results but I fear even this will noe help in my dead areas.

We are on chalk with only a modest covering ot top soil so any rain goes straight through hence the parched condition.

Anybody else in the same boat?[b][/b]