I think if it were me, I would put down cheap Supermarket/B&M’s patch repair (or use the links provided) given the time of year. Although seeds will germinate in as littles as 10 days, it needs 7-8 weeks at temperaturers above 8c for the grass to fully take hold. Probably worth a shot
If looking at it doesn’t distract you, you could add a fertiliser to your lawn during October and prepare and ressed your lawn next March, which will yeild a better job overall. Depending on the quality of grass you want depends on whether you view your lawn as ornate or a piece of everday greenery, which needs less looking after, then either the economy or the Superstar or family lawn variety from the above links.
A cheap lawn spreader will give you more even results and take advice from the 2 links provided. Both companies are helpful should you wish to ring them.
I had a more of an ornate lawn for my back garden but, it took alot of looking after and worse since Ive been ill, I’m now thinking of taking the easy way out and going for artificial lol.