This is not correct. There was a review done of the training scheme and a recommendation was made to change this. But without legislation, the most the DVSA can do is "recommend that riders take further training if they want to ride a geared motorcycle".
See item 6 in the table on page 8 of https://www.gov.uk/government/uploads/system/uploads/attachm...
FWIW, I think a staged CBT is a fine concept, especially in London, but there's a risk that an automatic-only CBT would make things worse because of the incentive structure.
In a busy urban environment, focusing on the hazards on the road should be a much higher priority than mastering machine control. Spending time on a scooter is a fine way to adjust to this. Moving on to a geared bike is less problematic as the amount of new input and reactions that need to be dealt with at once is reduced. But a split between auto-only and geared CBTs would probably push more riders to go geared sooner rather than later (to avoid prematurely limiting their options), and increase overall risk on the road. I think this is part of the reason for the prevalence of geared cars on the roads in the UK.
On the other side, if you learn to ride out in the countryside, there's no guarantee you'll be any good at handling the hazards of rush-hour metro traffic.