Cardiovascular work can be detrimental, but much depends; how hard, how much, how long, how used to doing it you are.
On so few calories, the body can break down lean tissue to provide energy which will reduce your metabolic rate (as well as not being a good thing to do from a health viewpoint).
There's also some rather complex hormonal changes that can come into play.
Basically, you don't have enough calories in to do a great amount.
Having said that, research points to resistance types of exercise being beneficial, helping to protect lean mass, so hit the weights.
I think most forms of swimming and walking are usually okay...just don't go mad. Anything in the way of cardio would need something more personalized set out by a PT who has experience of VLCDs. Not me, so I couldn't comment
But yes...it can have a detrimental effect on fat loss for a number of reason with so few calories going in.