I recently challenged myself to add reverse to my hobby lathe. It works well and was interesting to do.
It involved stripping down the motor to get to the individual windings, rewiring the on/off switch and adding a 6 pole drum switch.
The switch simply reverses the polarity of the secondary windings which starts it in reverse.
It was quite a fiddle and not to be taken lightly. Brass grubscrews in the faceplate will prevent it unscrewing and pressure from a running centre will stop the chuck from going anywhere.
Not a job I would recommend for anyone not well versed in electrical matters.
I hope you will now develop the habit of always securing the faceplate or chuck with the ‘brass’ screw to ensure it can never unwind itself if you go into reverse (on purpose or by accident - the latter being not uncommon).
I also hope that you are not using one of the belts made up of individual pieces - which are easy to fit and adjust for length but are only suitable for one drive direction.
Happy turning.
Nice job. 
As you say, not something to do unless you know what you’re doing.
I was quite surprised when I bought an additional faceplate from Axminster that it didn’t have any lock screws in the flange. I quickly remedied that situation by drilling and tapping my own M6 holes.
Thank you both for the encouraging replies. Having worked as a pattermaker using large commercial Wadkin lathes, it’s frustrating having a limited budget. Being able to reverse it will be useful - and cost less than £30!
Time to rifle through the log pile for something interesting.
This is great. I have the same lathe so will look into this.
Have you had any luck reducing the min speed of 500rpm so bowls close to the max diameter can be done if working with out of balance timbers?
