I'm surprised the BBC don't control the 'talent' side of things, even though the presenters technically work for the Met Office.
Similarly to when news contracts have changed on other channels and the presenters have carried on as normal.
It's the opposite to that situation though, and it's not just that they 'technically' work for the Met Office - they REALLY work for the Met Office. Particularly in the case of presenters who are also fully-trained and qualified forecasters.
In the news contract case the presenters worked for, and were contracted to, the broadcaster (say in the case of Five News and the ITN/Sky switch)
In this case the presenters don't work for, and aren't contracted to, the BBC, they work for, and are contracted to, the Met Office. Those with full forecast qualifications can (and sometimes do) have other roles in the organisation.