There is also a weekly outreach service in Parracombe, which is a 12-minute drive.
Post Office Ltd said it was reviewing service provision in the area and it would update residents when the review is finished.
It said Royal Mail closed the delivery office in September and had paid compensation to the postmaster.
A spokesman said: “Our area manager had also been working with the postmaster to help recommend where overheads could be reduced and ways to increase revenue.
“We regret that they have made the decision to resign as a postmaster and want to thank them for the service they have provided to their community.”
Royal Mail said the delivery office in Lynton “wasn’t fit for purpose with limited welfare for staff”.
“It moved to Barnstaple where there are appropriate facilities in place.”
It added there was a number of post boxes situated near the Lynton post office.
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