If its located to the side of the existing house - as opposed to being wholly behind it - the conversion may require planning permission.
You will need to rung your local planning officer up and discuss this matter with him and bring alone a map of some sort showing the outbuilding.
If its not proposed to link to this directly from the main house you may need to prepare arguments as to what exactly this is, since it would not be an extension.
If its not an extension to the main house it will more than likely need permission - converted sheds to habitable use is not part of the exempted development schedule.
In terms of materials, the first thing you may need to do is obtain a permission for what you're doing and this is going to cost you some money.
It is possible that the existing shed/laundry room has a proper foundation, but it is unlikely - so you're not converting really; it may be a total demolition and new build.
If you want to get second opinions for free you can, as I said talk to the planning officer, but they don't 'do' construction details - you need to speak to the Building Control Officer.
Building Control Officers seldom deal with buildings on an individual basis and you could be opening up a can of worms by talking to either of them - does the existing shed need permission?
ONQ.
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All advice on AAM is remote from the situation and cannot be relied upon as a defence or support - in and of itself - should legal action be taken.
Competent legal and building professionals should be asked to advise in Real Life with rights to inspect and issue reports on the matters at hand.