The airspace closure was done by NATS, not HMG, and only to IFR flights in class A airspace. Several jets (private / small charter) left U.K. airspace on Thursday and Friday VFR, low level. By Friday evening CAA (the governing body) were still advising that NATS closure was recommended and that if people tried to circumvent it a more general closure would be put in place.
Presumably, sometime over the weekend, CAA took charge? Otherwise , how did it become the case that it was the CAA spokeswoman outside of the DFT on Tuesday evening rather than a NATS spokesperson?