Great Northern and Thameslink trains serve centres such as London, King's Lynn, Cambridge, Peterborough, Hertford, Bedford and Brighton.
A shortage of drivers on Sunday meant many services were cancelled.
"We rely on drivers working rest days but on this occasion, it has not been possible and for that we apologise," a company spokesman said.
"Sometimes, such as at Christmas time and annual leave periods, we do not have enough drivers to carry out both day-to-day operations and the large amount of training required.
"We have been working flat out to address this with the UK's biggest driver recruitment and training programme.
"Currently we have 190 drivers being trained - 96 on Thameslink and 94 on Great Northern - and it takes more than 12 months for them to become proficient on their dedicated routes."
New electric Class-700 trains with larger carriages are to be introduced across the north-south route through central London from 2016, the company said.
A train company has apologised for cancelling services on one of the busiest post-Christmas shopping days.