A phone that actually costs less than $100 will make money from something other than its purchase price.

In some markets, that means the carrier subsidizing the phone and charging you a high monthly rate. I would counter that phone service should not cost more than $15/month.

The other thing it might do is preload adware, spyware, or outright malware.

It's barely economical to address it. Hard to pay off r&d and setting up production. Also, would probably require own Android fork or entire different OS with a lot of tradeoffs to run smoothly on ultracheap hardware.

I bought a new Nokia E63 for AU$199 in 2009 (around US$160 at the time). I liked that phone! It had a QWERTY keyboard. Replaced it with a Samsung Galaxy S3 in 2013.

$100 or even $200 is likely not doable for a modern touchscreen phone, unfortunately.

I'm willing to pay upwards of £300 max, but it should also include being able to have a SIM card AND an SD card, as well as a headphone jack.

For that kinda money, you should get yourself a flip phone. They still exist. ;)