Southern also has connections from London Victoria to locations such as Brighton and Eastbourne.
Southern's decision to suspend its London Victoria services will also mean services from Clapham Junction, Battersea Park and Battersea Park will also be affected.
Planned re-signalling work at London Victoria has already resulted in diversions for Southern Rail between December 17 and January 3.
These diversions have seen the London Victoria service run to and from London Bridge during the festive period when demand for travel is low.
Many other operators in addition to Southern have decided to cancel trains due to the pandemic, including South Western Railway, which also serves Portsmouth and said it was suffering a shortage of staff ‘across our business’ such as drivers, guards, engineers and controllers.
The firm warned passengers that its services were ‘subject to short-notice cancellations’.
It would introduce a reduced timetable from January 17 in an attempt to improve reliability.
CrossCountry urged customers to avoid travelling on New Year’s Eve as a strike by members of the Rail, Maritime and Transport (RMT) union means it will run ‘a very limited timetable’.
Cancelled services include those between Aberdeen and Edinburgh; Glasgow Central and Edinburgh; Derby and Nottingham; Peterborough and Stansted; Cheltenham Spa and Cardiff Central; Newton Abbot and Paignton; and Plymouth and Penzance.
RMT members employed by Gate Gourmet will also be involved in a rail strike at Edinburgh Waverly on New Year's Eve after a long-running dispute over allegations of bullying.
RMT general secretary Mick Lynch said: ‘The disruption to services from the New Year’s Eve strike action is wholly down to these greedy private companies on our railways seeking to squeeze out every penny they can by hammering down on safety, jobs and workplace dignity.
‘Our members at CrossCountry and Gate Gourmet are standing up for all rail workers as we expect a torrent of attacks on jobs, pay, safety, pensions and working conditions in 2022.
‘We are ready for a new year of campaigning and action on all fronts.’
A ‘heavily reduced service’ for CrossCountry will be in place between Edinburgh and Plymouth; Manchester Piccadilly and Bournemouth; and Birmingham New Street and Peterborough.
The dispute involves train managers and senior conductors in a row over the role of guards.