I think it depends on what type of lawn you want and what it will be used for. For example, will it be used by children for playing football or do you want a beautifully chequered lawn that is lush and green?
Go to a garden centre and have a look at the different types of seed for different use lawns.
I got a box from B and Q several weeks ago and sowed it immediately. I reckon not a quarter has come up. I have sowed grass seed many times before, and never been so disappointed. I can still see seeds on the soil which has not sprouted nor been eaten by birds. Grass seed is supposed to be treated to make it distasteful to birds, by the way. I suspect that this seed was old, but there was no "sow by . . " or "use by . . " date on the box. I looked very carefully.
If you are going to have a lot of traffic or kids playing a rye mix seed..I used an ornamental grass seed as my lawn is not played on at all...you will need to prepare ground well , water first ...and keep watered in this weather..protect by making paper tags strung across area ...