I need a part time job. Spontaneous application?

[FeetOnly]

I am going mad, sahm for 14 years, one bout of 18 month temp contract a few years ago. I have a DC with SN so realistically cannot work more than 40% and only Mon-Fri standard hours. I think we could cover 2 days in the holidays with MIL and DH wfh+ screens and DC should be ok alone for an hour or so with Netflix. There are two afternoons a week I wouldn't be able to work (DS therapy) and I don't think I could start until October at the earliest, to give Dc time to settle into secondary.

How do I go about this? Will any company take me seriously? Is it too early to send out letters?

There is little point sending letters out now if you don’t think you would be able to start any work until October.
You would be best to use the time between now and then to brush up your skills with some courses related to whatever job you’d like to do, and maybe volunteer somewhere for experience.
Nearer the time start looking at job vacancies.

if you Google courses for reentering the workforce several things come up eg
https://womenreturners.com/skills-updating/free-online-courses-to-support-rtw/

The WEA (charity) also offers workplace skill courses online, many of which are free/funded:

https://enrolonline.wea.org.uk/online/coursesearch.aspx

If you just want to see work courses leave all the boxes blank except the last one: Under the "be inspired" heading select "work related".

You can filter to "online only" courses or include your postcode to search for in person options too.

@RoddyStJames when is the right time to apply? I've honestly no idea what kind of job I could do. I would need to find something very local, I think, in case of emergency and there's not much of the industry I'm qualified in. Although it was so long ago, I'm not sure it would be any use now. I've forgotten most of my degree! DH would never agree to picking up the slack just for a volunteer job.

will take a look at those links. Thanks