Shredded woody prunings as mulch?

[WhereDoesThisToiletGo]

Fairly clueless gardener here.
Like many people at present, I am doing more gardening than usual with the universal problem of no green waste collections or Tip to go to.

A month ago I started off my purge of the garden by cutting back overgrown shrubs. I let the skinny branches dry off for a week, then fed them through my garden shredder to reduce the bulk.
I've now got a decent sized bag with a mixture of shredded material. Some fine and totally dead wood chippings and some ribbony shreds from stuff that was most probably a bit too green.

My soil is not great but the local area is all stony soil that dries to either dust or concrete!
Can I spread my chippings over my flower beds as mulch , it might not improve the soil but it might discourage weeds.
I don't want to do it if it's an actively BAD idea.

Many thanks for any advice

www.rhs.org.uk/advice/profile?pid=635

@Unravellingslowly Thank you, that's a very useful source

Advice is not to apply to dry soil in summer. If you have space to keep it, fine, if not, wait till there's been enough rain to wet the soil, and then apply the mulch, at which point it will help reduce evaporation.

@MereDintofPandiculation Thank you. WE have rain forecast at the weekend, I'll leave it til then