The ash from your charcoal will have no beneficial effect, but you are thinking along the right lines. Now if you crush the charcoal and add that to your compost bin several processes will start to take place. The charcoal will absorb the breakdown products of the decomposing vegetable waste. Then mycorrhizal fungi which have a symbiotic relationship with carbon produce a glycoprotein called glomalin. Glomalin causes the compost to adhere to the charcoal and the soil to which it is introduced. It is my belief that this how the natives of the Amazon delta created Terra Preta.

Having said that UK conditions are far removed from that of the Amazon, high temperatures and humidity may be necessary to create Terra Preta.

I am just about ready to start trials but my process will be quite different as there are other ingredients which I view as being necessary in the recreation of this self sustaining soil.