In the petition, Farron wrote that the Post Office was a “vital service” which needed to remain “where it is” or have “suitable premises”.
“We can’t go back to thinking it can be downsized and stuck in the back of WH Smith,” he wrote.
Three years ago, Kendal’s Post Office was at risk of being absorbed into a branch of the stationery shop.
Farron has also said the upcoming loss of High Street banks Halifax and Lloyds in Kendal next year would make the Post Office branch even more important for residents, according to the Local Democracy Reporting Service, external.
However, there are still a number of bank branches in the town, including Barclays and HSBC.
Business and trade minister Gareth Thomas said “no decisions” had been made on any specific Post Office branch as of yet.