From what i have actualy seen so far i see no evedance of martial law being imposed.
these are the official plans
In the time it takes to develop and procure the new vaccine, the following measures would be used to try to buy time and stop the virus spreading:
Travel between the UK and infected countries restricted and health screening begun at ports
Infected people asked to go into voluntary isolation and those who had been in contact with them into voluntary quarantine
Public gatherings such as football matches and concerts restricted, along with movement of people within local areas
Schools closed
Infected people, those who had been in contact with them and possibly the general public told to wear face masks.
bbc
it talk of voluntary isolation, but im not sure it would really be so voluntary. Their would atleast be alot of pressure put on the individuals to go
in of their own free will.
Because the Military would probably have a big part to play in the plans i would say that justifies the minister for defence becoming involved.