Batty,
To my mind,
JAR OPS 1.340 prevents you departing for your destination in your CAT 2/3 a/c if you do not have an alternate
at the flight planning stage (
JAR OPS 1.295) that meets the prescribed planning minima in
JAR OPS 1.297.
In this case, it would need to be CAT 1.
However,
once airborne, the relevant legislation is
JAR OPS 1.400 & 1.405, whereupon CAT 3 weather at your alternate does not preclude you from using it.
Perhaps you are confusing what is legal at the planning stage and what is legal once airborne?
Just a thought.