I often hear people talking about the gym and VLCD and whether it's worth doing them at the same time. Something a lot of people talk about is how the gym will help you look more toned, less skimpy fat etc. talking about building muscle.
When you're on a VLCD you're getting everything that you need but that's basically just to keep your body going on a normal day and be healthy. If you up your calorie burn a lot, you're actually risking doing your body damage. You're only getting around 600 calories a day, that's well under what you burn even if you stayed in bed all day. You just don't have the fuel for gym sessions too. If you do really want to go, keep it shorter and not too intense or just stick with swimming, which isn't as debating but is very good for you. Otherwise you could find yourself getting ill.
To address the whole toned/muscle issue... To look toned you need to get rid of fat and build muscle. That improves your BF%/fat to muscle ratio. The gym and particularly doing resistance/strength training is great for doing that but to build muscle you need a decent amount of protein. With the amount of protein that you're getting with these packs it's physically not possible to put on muscle.
Personally I'd do what someone else said they did. Hold off on the gym for now, it won't really help you at the moment. When you're getting close to goal, that's when I'd start going to build up your gym sessions and get yourself into those good habits for maintenance. That's the way that I personally think would be best. Good luck whatever you decide.