Johnd: October is getting a little bit late to reseed a lawn, especially if the ground needs a lot of TLC preparation beforehand. However, it's a great time of year to put down turf (the ground preparation is still important though) - because:
1) the turf will grow more slowly and therefore more thoroughly embed than, for instance, during a summer drought and heatwave.
2) because of the usual climatic conditions prevailing in autumn it doesn't need the usual watering and lengthy "keep off !!!!!" period required in summer.
3) as turf is a bit fragile until it's growing robustly there is less risk of a devastating frost in October than in the later months.
Grass seed will be patchy at best at this time of year because of hungry birds/cold conditions.
Downside of turf is the expense over the cheapness of grass seed.
Whichever you choose, make sure you get the correct grass variety for a normal back garden family lawn. Differing varieties - ie. coarse, bowling green, roadside - are important. You need hard-wearing but attractive.
Bit of research required for a good domestic lawn. Expensive mistake if the variety is wrong.