welcome to the group Caprifool
I agrees that washing machine looks in great condition and I've not seen one with a timer fitted either, though it makes sense that hoover could have fitted them, as it's the same combined switch and timer fitted to a hoover twin tub I bought back in the spring of a similar age.
So to the pump impeller, using my calipers it looks to me that the shaft would be a quarter of an inch, as the bearing I've found measures to 6.25mm. That makes sense as back then many parts particularly shafts and bearings were made in imperial measurements.
However, I do have a several of these replacement impellers, as I did manage to buy a bag full some years back, if you'd like me to send one, email me an address to post to and you'll be welcome to have one. Also if you would like, I have a spare hose that fits onto the outlet behind the wringer you'd be welcome to.
Mathew