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Replace bathroom extractor fan and vent to outside

I live ina two storey 1930s house. The downstairs bathroom fan currently vents into the roof, and I'd like to install a new fan (existing one is fairly old) and vent it to the outside. This should be possible as the house has overhanging eaves. Access to the roof space is possible through a small door that you need to crawl through. The current extractor fan is operated by a switch (part of the light switch on the wall) which ideally I'd keep - but open to suggestions. Thanks.