Is it a CSA platforms, CSA retail/lounge/floorwalking or CSA Onboard? I've held 2 of those positions and sat the test for the 3rd, so unless things have changed much since then your day should be something like this.
At the start you all do some paper tests - there are different ones for each of the 3 types of CSA. Platform staff have to do the dispatch test, retail a ticket selling test and Onboard a slightly more simple maths test. All 3 normally also have to do a test showing how well you pick up and understand rules. The papers are marked straight away, and those who pass go through to a group exercise.
Normally, you are all put in a room together, and you get given a story. It's usually something along the lines of your boat has sunk and you have to pick which objects are the most important to survive, or the world is about to end and you have to choose from a list which people you would save. You get given a few minutes to make your own rankings, then you all discuss it as a group and try to reach a consensus together. It's a good way of seeing which people are too quiet or timid to get their voice heard, and which people are too dominant. Communication and team working skills are vital so thats what you really need to demonstrate.
Those who pass that, get to go for an interview.
I can't guarantee that's how it will be, Euston like to do things their own way(I know for their recent TM assessments they added some extra things that the other depots don't normally ask for), but for most Customer facing jobs at Virgin, the routine is something similar to that.
In any case, good luck! Which ever job you are going for, they're a great company to work for, and whilst the jobs can involve a lot of hard work, they're also great fun and very satisfying.