I think the easiest way is to add another step after using the Army Painter wash: glazing with inks. These can be found in much more saturated colours and make sure you don't end up with a muted end result.
So:
1. paint your miniature and make sure you have bright and light highlights.
2. Apply Army Painter wash to shade the recesses.
3. Apply several thin ink glazes to make the colours more intense, draw the colours more together and get that more saturated look.