I have now had a reply from the Sunday Times Crosswords Editor. I shan't attempt to summarize it - just copy-and-paste:
"We have decided to accept entries for both 3222 in print and 3223 online this week, with both contests closing at the end of Saturday, and that 3223 in print and 3222 online next Sunday will both be non-competition puzzles.
As an entry for 3222 in print, it's fine to send an email to the stated address, with a scan or attachment of your handwritten solution. It's also OK to send a typed solution in a format similar to the one used in the paper each week.
The key point is that you must include the correct puzzle number in your entry to ensure that it's included in the draw (done automatically if you type up a solution online). As we have had to make both 3222 and 3223 acceptable numbers for that purpose, an entry making the same mistake that someone here made and confusing those two numbers will end up in the wrong draw.
You can also enter for 3223 if you want, and the online versions include print options if you prefer to solve that way."