Do I Need to Replace Soffit Board

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My neighbours recently replaced their roof (pitched) and at the time we did not notice that there is a hole in the soffit board that adjoins their roof. It was not caused by the work that they did as it looks like the wood has been rotting a little for a while. This is in the corner where the party wall is with their property. We have no leak in our loft - do we need to replace the whole soffit board or can we remove part of the wood and then fill the gap to stop birds and water getting in? With winter coming we need to get it sorted. Is there a cheap way of doing this or will we need to call in the builders/scaffoling etc - and how much can we expect to pay? Any cheaper alternatives would be greatly appreciated. :rotfl: