To assist one will give a realistic indication as to time lines.
Usually, without any dockside problems, or a medical emergency, self disembarkation is approximately 1.5 hours after fully docking, UK Customs ship inspections/procedures and luggage offloaded.
Collection of suitcases from terminal and the queue to go through to Customs, is about 30 minutes.
Allow 3 hours for journey without any comfort break, because of morning Southampton and usual London traffic.
No allowance is made for late docking, extra heavy traffic or motorway and/or road accidents, which will cause delays or detours.