It would depend on the other animals in the wood. The number of dormice would obviously decrease and if there was another consumer of dormice in the wood the number of these would also decrease - because of food competition. Anything on the same level as the dormice would also decrease if there is a secondary consumer, (other than the owl) which eats this.
and of course if the population of dormice dropped to such a level as to not provide enough food for the predators, then the predators would tend to move on elsewhere or not raise so many young. Nature tends to balance itself out in this way- unfortunately it all goes to rat poo when man pokes his nose in!