You don't really have to worry about frost in the UK and it is almost always raining once a week!
The current heatwave is a big factor right now though.
I'd wait until the beginning of September when the edge is off.

I always thought you could overseed and then topdress at the same time so there is more seed to soil contact.

I could be wrong though, I haven't lived in England for 10 years. What do others think?

 

Go for it now as long as you can water, no reason to delay. For the past two years I've either done a full renovation or overseed mid August with temps 25-35C, no issues. Just water 4 times a day. If you overseed between now and mid-August, you can get your first cut in early September with a fertiliser treatment once you cut. Avoid the starter fertilisers.

If you only need a light top dress, then seed and top dress over the seeds, but lightly (1-5mm). If you are looking to change levels, best to do that in Spring.

Why do you need to aerate?

We have had the driest July in over a 100 years, not sure why people think its always raining in the UK, maybe in Scotland