I am guessing that wasn't the new price from Tesco
No, but one of them was free after being found abandoned outside a Tesco (done through the police) That's the one that had all the parts. The £26 one was £26. However you didn't dismiss the bike on the basis of being from Tesco when you said
If I had a 2 mile commute and only £100 for a bike, I'd just walk to work while saving up for a decent bike
You appear to be dismissing all bikes that are cheap as being not 'decent' The OP seems to have accepted that second hand is the way to go.
Obviously at that price you're not getting anything fashionable, but it was enough for a Tange-tubed mountain bike with 21 working gears and decent tyres and brakes that work. The frame is sound. Everything else is a wear item.
OP - I've weighed my rucksack from today and it was about 9kg - laptop, SLR, power supply, laptop bag inside rucksack, rucksack itself. I'll be honest, when I put it on each ride I curse, but you soon forget it. You cannot ride with that on your back and wear the same shirt for work in this weather though! It can be done, and if it's really on two flat miles then I'm sure you will be fine without panniers. Aldi do them every year at some point, so see how you're getting on when when they appear.
eBay and small ads are great for secondhand bikes, but you have to be careful you're not buying a stolen one. Ask questions. At the age of bike you might get (mine are 25 years-ish) you can't expect receipts, but at least get a plausible story as to the provenance of the bike.