"despite the lack of infrastructure to support them"
There's precedent for the increase in demand - the widespread adoption of air conditioning.
As long as demand increases no faster than the leccy network can be built out then it will work
UNFORTUNATELY the move away from oil/gas heating has to be factored into it too (nobody will buy reticulated hydrogen - it will be at least twice(*) the price of electricity vs current retictulated natural gas being 1/3-1/5 the price of electricity)
AND even if the distribution network is built out in time at both core and leaf level (street level infrastructure has about 1/3 of the needed capacity right now), there's a hellbent mentality of using "renewables" and resisting nuclear power (in particular, a marked lack of enthusiasm for alternatives to the weapons-derived/weapons-enabling uranium cycle we currently depend on)
Britain _alone_ needs at least 70 new GW-scale power plants for baseload (including replacing the aging out ones). Good luck doing that with wind and solar, no matter how many battery banks are used to balance their generation/non-generation abilities
(*) No matter how expensive electricity may get, "green/blue" hydrogen will always cost more. It's vastly cheaper to generate electricity from the energy sources involved than to make hydrogen. The safety concerns of hydrogen don't overly matter if nobody will buy it on economic grounds