This process takes up to 2 hours as long as it is during the porting hours.
8am to 6pm - Monday to Friday
10am to 5pm - Saturday to Sunday
If you request to port your number outside of these hours, you can still submit your request, but your clock wont start until the next morning. You should not lose your service with the existing provider during this time.
When your number is moved over to Virgin media you will lose service on your old sim. You should then put your new Virgin Mobile SIM into your unlocked phone and you should be good to go!