Obviously the devil is in the details, i.e. what it will mean exactly "after the cutoff date": if one has lived in UK long enough to qualify for treaty-rights but never actually exercised them formally before the cutoff, can he still do it after that date? That's the situation most people are likely in, at the moment. A reasonable government would answer yes, of course, but recent news seem to indicate they are looking for any excuse to kick people out, so it's not a given.
If you are an EU citizen living in UK, you should absolutely ask to exercise your rights TODAY; do not delay, do not trust news reports, it's just a bit of bureaucracy but could make a big difference in your future. Make sure you send documents as recorded delivery and track each and every date.
If you are an EU citizen looking to move to the UK: just don't. This country has decided they don't need you and me, they don't deserve our labour, our ideas and our taxes.