Rail passengers from Huntingdon and St Neots will be in line for additional compensation because of the chaos caused by the introduction of a new timetable.
Govia Thameslink Railway (GTR), whose trains stop at the two stations, unveiled the compensation scheme for passengers most affected by disruption to services which have seen trains cancelled, running late and being replaced by buses, since the ill-fated shake-up of the timetable came into effect in May.
But GTR, which will administer the scheme, said it would start to contact qualifying passengers by the end of August.
The move came as GTR set up a new interim timetable on Sunday which was designed to make services more reliable.
Under the compensation scheme, refunds are being offered to customers, in agreement with the Department for Transport, and will be on top of the usual Delay Repay compensation for late journeys.
The scheme will be funded by the rail industry, including GTR, with the amount of compensation being paid according to the level of disruption since the May timetable was introduced.
Qualifying passengers will have to have held a season ticket for travel between May 20 and July 28 and will receive a refund based on the equivalent cost of one to four weeks' travel.
GTR will administer the scheme for the rail industry and will start to contact qualifying passengers it has identified by the end of August and will advise them of their refund amount and seek payment details.
The scheme will then be opened later for passengers to submit claims.
Nick Brown, GTR chief operating officer, said: "We apologise to passengers for the poor level of services since the introduction of the May timetable.
"In recognition of this we will be refunding fares according to the level of disruption on Great Northern and Thameslink routes. This compensation is offered in addition to our usual Delay Repay compensation for journey delays of 15 minutes or more and enhanced compensation for season tickets holders."
GTR said the interim timetable marked a significant stage in its recovery plan and was committed to running more peak hour trains and a more regular service.
South Cambridgeshire MP Heidi Allen Tweeted: "Today is the beginning of @GNRailUK new interim timetable and must show significant improvement on what we have been experiencing. If you are a constituent and things are going wrong, please e-mail my office so I can gather evidence."