Unfortunately, I’m not sure, I can be of much help, as we didn’t use public transportation, but went by car to and from start and end points. For detailed information about public transport, have a look at the official South Downs Way Public Transport Guide

You should find decent hill training all along the trail, but for what it is worth, and this is from memory only, I think Alfriston to Eastbourne (with Friston Forest and the Seven Sisters) and Upper Beeding to Pyecombe might provide decent hill training.
Have a look at the elevation profile on the Bikedowns website, which should help you choose an appropriate area.

I hope the above helps and that you enjoy the South Downs.

I would be very grateful if you could offer me some advice about the South Downs route.

A group of friends and I would like to get some hill training in before we attempt the Three Peaks (Ben Nevis, Snowden and Scarfell Pike). We live in London, and so the South Downs would be a convenient training day.

Could you give us any advice as to where the steepest/hilliest section of the South Downs is, that would be convenient to reach from London by public transport? Any clues very happily received!

Thanks very much for your help.