What is best to mulch with in autumn if you want some nutrition and are mindful of cost?

[Gibgertea]

Any online recommendations?

...make friends with a tree surgeon and ask for free wood chips in exchange for a cuppa.

Or put your request up here:
https://freewoodchips.co.uk/

Woodchip (especially ramial I.e. from small younger twigs)
Sow a green manure if the ground is clear now- clover or field beans both great for nutrition
Chop n drop what you already have

Green Waste compost from your council is more expensive than the above but also an option.

The trouble with green waste compost is that you don't know what's in it. Could be traces of weedkiller that was used, and then the dead plants composted, or there could be lawn treatments in grass clippings. Composting does not get rid of those chemicals.

Using the spent compost out of your own summer bedding containers and hanging baskets is something I've done for a long time, and although it doesn't add all that much in the way of nutrients, it is good for improving the soil structure.

Fresh woodchips deplete nitrogen in the soil as they decompose, so it is better to use composted bark instead.

If you live near some stables, there's always horse manure.