My late Dad and Uncle so believed in this method when I was a kid growing up .

To this day I still have a diluted bottle handy to use Ralphy.

Yes Ralphy, I have used this method to control pests for many years. It works fine for me, it's cheap and it doesn't involve the use of nasty chemicals as such. Just about every year I get an infestation of what looks like black fly on my cherry trees and a quick spray of dilute washing-up liquid does the trick.

Soap solution will see off most soft bodied arthropods Such as aphids, mealybugs and spider mites.

I believe that the way this works is that it effects the membrane of the insect and can also break down the protective wax covering causing the insect to lose water and ultimately die.

I too use this method for aphids on my plants such as roses.
I make up a soapy solution and add a drop of veg oil as it makes the solution sticky to keep it on the plant a bit longer.