First Capital Connect said it was running a "near normal" train service after drivers accepted a pay deal.
Members of the train drivers' union Aslef had been choosing not to work overtime, disrupting the Thameslink route between Bedford and Brighton.
Many trains were also taken out of service during the recent bad weather, with snow and ice causing power problems and sliding doors to freeze.
The company said it would compensate customers who were affected.
Gareth Beazant, from First Capital Connect, said: "We are now looking at an improved compensation refund package and further details will be made available as soon as possible.
"In the meantime we are advising customers to keep their tickets."
The company's website states that any customer can make a claim for a journey delayed by 30 minutes or more.
In recognition of the "extreme disruption" for season ticket holders, a plan for additional refunds was being finalised.