Both trees were found to be suffering from Dutch elm disease and the local authority will send the timber to the government burn site to help prevent the disease spreading further.
Chairman Steve Curphey said the trees were ‘iconic’ and had stood long enough to witness both the first train arriving in the village and the last train leaving it.
‘A lot of planning was involved in getting one of the trees felled, and we then realised the other tree also had Dutch elm disease,’ Mr Curphey said.
‘It’s a very sad day because a lot of residents have fond memories of playing in the tree as children. I played in it and even fell out of it as a child, while this year people also sang Christmas carols beneath it.
‘It's been such an iconic part of the village for so long. If you look back through history, it has always been there. It sits on the old railway line and now there’s going to be a big open space.’
Dutch elm disease is spread mainly by elm bark beetles, which carry fungal spores from infected trees to healthy ones. It can also spread through root grafts, where the roots of neighbouring elm trees naturally connect underground.
Plans are already under way to replace the two trees in the children's play area.
Mr Curphey added: ‘We're hoping to have the stump of the larger elm carved, and then we're going to replace the two trees and dedicate them to two local heroes.
‘We're going to put that out to residents, who can then choose who the two trees should be dedicated to.’