The problem with the 3 gang converter in your utility room is that it is fitted with a 13A fuse protecting all 3 sockets- that means the combined load on all 3 sockets should not exceed 13A. Your washer and dryer together will be doing between 16 and 26 amps- bit of a mismatch there, no wonder the fuse carrier is getting hot.
The 2 gang converter doesn't have a fuse in it, running 26A through it all the time won't be sensible but theoretically won't overload it (though if you do buy one, do read the detail about what current it is designed to safely carry).
3 gang converter in the bedroom supplying (say) a reading lamp, phone charger, alarm clock- no problem there, total load about 1 amp. Even using an extension cable is fine as long as you're not using multiple heavy current devices on the 3 gang converter.
The 2 gang converter doesn't have a fuse in it, running 26A through it all the time won't be sensible but theoretically won't overload it (though if you do buy one, do read the detail about what current it is designed to safely carry).
3 gang converter in the bedroom supplying (say) a reading lamp, phone charger, alarm clock- no problem there, total load about 1 amp. Even using an extension cable is fine as long as you're not using multiple heavy current devices on the 3 gang converter.