Those who have the right to work are those who have requested it successfully after 12 months, and those who were lawfully in the UK on a visa that allowed them to work when they applied for asylum. I.e. all the "small boats" asylum seekers don't have the right to work by default and they are perfectly allowed not to request it.

The announcement is therefore a little disingenuous (or more than a little) but that's politicians for you.