Sorry but you cannot compare a local personalised shopping service to delivery/deliveries from Tesco based on price nor any other single supermarket or single purchase from the likes of Argos etc.
I very much doubt OP has the logistical support available to a major supermarket so obviously cannot compete on the price of a delivery from one provider only. That would be ridiculous.
Also, since when will a Tesco delivery driver pop into Aldi and Argos on the way to drop your groceries off.
Offering to go to any shop needed is not the same thing at all as deliveries from Tesco only.
OP is offering a service to people outside of single shop deliveries. I am assuming, this is aimed at people who would otherwise have trouble accessing such shops/delivery services because of things such as no vehicle of their own, mobility issues, time issues, access problems or any combination of the troubling life problems that form a massive pain in the arse if you need anything unusual fetching for you.
I think it is a very good idea if you can get the clientele numbers to make it worth it.
I personally would not be charging just £1 to drive to Argos or similar to do Click and Collect though. That's selling yourself a bit short unless you have a lot of pick ups from the same place.
Tell you what people with issues have trouble with.
Getting semi awkward stuff that's a bit on the larger side, like a small carpet/chair/TV/etc and actually having someone willing to carry it into your house rather than just dumping it on the kerb outside your front door. Maybe look into a small van and a strong helper for the future if the other part takes off.
And, no, I don't think you are charging too much.
Good luck.