A little wood ash is ok on your garden but not where you grow crops. Ashes from wood may raise your soil pH because about 25 percent is calcium carbonate, you can use if your soil pH is under 7.0 you may need to do a soil test? Wood ash does not contain nitrogen.

Wood ash is fine in your compost and we keep pure wood ash aside to mix a small amount with potting compost.

on g.w they said no coal ash , agree with m.g my mum used to put ash on the borders she was very gree fingered

Absolutely no ash that has anything other than wood in it, will pollute the soil.

In the U.S., in general, if you garden west of the Pecos River, and east of the Coast Ranges or Cascades, your soil is likely to be too alkaline to use wood ash. Elsewhere, it's worth a try, as long as you water well afterward.