Red Spider Mites?

I put a spoonful of cooking oil and a spoonful of fairy liquid into a sprayer full of water today and gave the rose and the dahlia that was next to it a good soak. I also sprayed a couple of spare pepper plants to make sure that it doesn't hurt the plants, because there's some yellowing on all the peppers that I fear is down to the spiders as well.

If nothing dies in a few days I'll start regular repeat spraying and see what happens.