This process takes up to 2 hours as long as it is during 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 it will be handled the next morning. You should not lose service with the existing provider during this time.
When your number is moved over to Virgin Media, you'll 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!