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Knockdown existing kitchen and conservatory and build a new single-storey extension off the back for kitchen diner, and open out the two rooms that face the back of the house to make that open-plan
Leaving the existing rear wall in place would help massively on budget and there is a question of really how big any one room needs to be. If you build across the whole back including where the WC is you’d have a (?) 25 sqm room which I think is more than big enough.
Doable with some change from £100k depending on how fancy you get with cabinets, appliances and glass roof / bifold / crittal.
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