In theory, you can dig a basement under any house. In practice, some properties are more suitable than others.
It's easier if you already have a cellar. It's easier if you have a suspended timber rather than concrete floor. It's harder if your house is constructed on bedrock, which takes longer to cut through. If the property is on a flood plain, construction will be much more complex.
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It's worth considering using a specialist basement company to do the job for you.They are set up to do exactly this job and, as they do one after another, they are more familiar with problems they might come upagainst and how to overcome them.