"We are very sorry for any disruption this causes to your journey today."
Customers were advised that the 281, 131, 57 Kingston, 71 and 465 buses will be accepting South West Trains tickets, while rail replacement buses would also be available.
Angry passengers took to Twitter to voice their frustration over the cancelled services.
Ray Rosario wrote: "Why do we have to put up with this every time there is heavy rain? Surely its about time something was done to fix this properly."
Elizabeth Gant said: "@SW_Trains thanks. 4 GCSE students are in a taxi to school. Will submit receipt to SWT. No buses at Hampton."
While Glenn Turner tweeted: "@SW_Trains where are these buses? Got told from ticket office to make own way to Walton or Staines Stations at own expense- joke."
And another Twitter user posted: "@SW_Trains again? Every times it rains, it's not like we live in England where it rains all the time."
Lines had been reopened by 9.45am, but customers were warned to expect delays and cancellations until at least 10am.