I agree with the contributors above but will add my threepennyworth about conformance to Building Regulations.
Conservatories are virtually impossible to get to conform to Building Regulations on the thermal performance requirements - the glass roof lets through about 10x more heat than your existing roof. This is not an issue with an added conservatory because such structures are classified as 'non-habitable' provided the existing external doors (often patio doors) are left intact on the dwelling. However, unless your existing garden room has an external-quality door separating garden room from whatever adjoins it, the proposed change will result in a breach of BR, quite apart from it being impossibly cold in winter and dragging the temperature down the temperature in the adjoining room.
OK - so does that matter? - maybe not to you, but come the time to sell the house, any surveyor will pick this up. This change will reduce the value of your property.