I have worked in the energy sector for all my career on the pipes and wires side. At one point I was responsible the design and capital investment program for the National Gas Transmission system originally built to bring natural gas to the UK from the North Sea fields. In the 90s and early 2000s this network was expanded to respond to the "dash for gas" which refers to the significant number of gas fired power stations being built that contributed significantly to carbon emissions by replacing coal fired generation.
The electricity challenge is not just transport but space heating where the peak gas demand is 4-5 times the current peak electricity demand. One of the proposed solutions is to shave the heat load peak by smart control of car batteries, so your car battery will be used to power your house heating at say 6-8 in the morning - oh dear then you have no power to use the car for a while.
The electrification of all our energy needs has major impacts on the electricity infrastructure not only on the network side but also in the home, you may need a bigger cable or a 3 phase supply if you have a high heat pump load to heat your house and several car charging points for your family. So this is why the government is supporting test projects and research into repurposing all the natural gas infrastructure for the distribution of Hydrogen - the big challenge the production using green power. Hydrogen boilers already exist - the pipes to get it to your home already exist it makes economic sense.