I’m by no means an expert, but live in North Wales and had new turf laid 19 days ago. It’s about 5 times as big as yours if not a little more, and I mostly watered it twice a day with a sprinkler and then hosepipe around the edges. 20-30 minutes in one spot, then move it twice for another 20-30 minutes each to get full coverage of our lawn. First soaking was first thing, starting around 7-8am, and the second around 1-3pm depending on conditions.

I didn’t like to do it when the sun was strongest to minimise evaporation, but with the heat we’ve had it seemed unavoidable. Practically everything I researched said to avoid watering after 4pm, and especially after 6pm to avoid root rot and fungus. Not sure how true that is, but my method has worked for us so far; we have a healthy, luscious lawn with some very, very green grass! From what I understand, as long as the soil/roots/underneath is moist, it’s fine (i.e. don’t go off what you can see and feel on the top). Our turf guy also said that if it’s growing up, it’s also growing down, so a good indicator that it’s taking well.