Would carpet and underlay go over old laminate flooring? There is beading along the perimeter by the skirting board which would presumably have to come up. Would all the laminate need to be stripped out first?
Only issue I can see (and that's as a strict amateur who owns some laminate) is that in the event of a problem needing underfloor access (gas fire repair/leak in central heating pipe) you'd have to take up the carpet and rip open the laminate: may be a pain in the a* refitting the carpet after that , as laminate doesn't easily come up and down and may fall apart. But from an insulation point of view your idea sounds great (as long as it doesn't lead to a "step" where the carpet is way higher than any uncovered laminate).