A power harrow is magic if the ground is light sand or silt and dry . If he is able to PH it and you can leave it a month or so to settle down you should have a fairly even lawn area . Weed kill it several times till the beginning of September then at the end of the month sow your seed . Do calculate the amount of sed neded and always allow for say 5 % more seed so you can reseed as needed later on .
take great care as tot eh quality bof grass seed you want as theyr are all manner of mixes .. To my mind most of the big store lawn seeds are not much use as tye contain a lot of coarse rye grass seed & not much fescue. If it is going to be a big lawn think of a commercial supplier and phone them for advice .
Where I used to live near Wisbech Cambs 18 years ago the big lawn area was about 76 x 40 mtrs & took three 10 kg sacks of seed costing nearly £340 . Luckily we had a real good old fashioned seedsman & hardware store run by a guy called MR PEACH close by to us
If you want to get it to bowling gren level you can still have th PH done , let it settle and then staret your compacting and levelling by walki ng up and down 10 sq mtr at a time then using "boning rods & adhesive tape" and a 6 foot spirit level sat on a 8 inch wide 20 mm thick saw bench cut * foot long length of ply or hire a dumpy level , to ensure that the trampled ground is flat . Let the weeds come through and hit them with round up three of four times between now & early September . Sow your seed in late September and lightly scratch rake it in with a spring back rake .
A lawn sown in September had a far better opportunity to germinate and sink decent roots down than a spring sown one that may suffer from a drought in summer . Plus there is less urgency for you to walk over a wet late sown lawn before it is rooted than a spring one that you think is long enough ( 2.5 inches ), ready for cutting & using straight afterwards .
The September sow lawn is good to cut late February , early March on a consecutive second dry day when it is 1.5 long ... the root system will now be sufficiently anchored in the ground . Take a second cut when it regains 3 inches tall .
Always make sure the mower blade( s) is/are really sharp for the best cut as a blunt blade will try and drag the new grass out . Any bald patches can be easily over sown after this first cut and again lightly scratch raked in . .