When I went for my Class One, I had just passed my PPL and was keen to do some flying and take some passengers (I had been flying on a CAA Class Two, which wasn't valid for licence issue).
Whilst I had to wait a week or so for the Class One to arrive, they gave me a Class Two there and then. It's worth knowing in case it comes up again. The tests they need to analyse for the Class One issue are not needed for the Class Two, so they could have given you the Class Two anyway.