Heating from gas is quite peaky (morning and evening heating cycles), whereas heat pumps are best when run low-and-steady.
Assuming 2/3 of residential heat demand transitions to heat pumps, and assuming an optimistic COP of 3 in the worst weather (highest flow temperatures, lowest air temperatures ... perhaps more like 2.5), then the power required to heat this fraction of houses is 2/3 / 3 = 2/9 of the mean gas demand. [0] linked report figure 1 shows a (smoothed by eyeball) demand of around 140GW "local gas demand" during the Beast from the East. This implies heat pumps would take over 31GW to power, which is more like 60% of the current UK electricity supply.
Sorry, alignment issue! Probably transport is less troublesome as it has a decent element of demand side response to it (batteries sufficiently large for a couple of days without charging).
It's not apples-to-apples though due to the difference in heating efficiency. If you use N kWh to heat your house with a gas boiler, you'll use N/P to heat it with a heat pump. P is something like 3 or 4, depending on various factors (and who you ask).
Plus housing insulation. So many British houses are still almost entirely uninsulated. That's not an exaggeration, the roof of my house had zero insulation, solid brick walls, no under floor insulation and single glazing. The only gesture to efficiency was some secondary glazing over the windows.
It absolutely ripped though gas just to keep a couple of rooms warm enough to live in, and it was still two jumpers and thermal trousers indoors. God only knows how the pensioner who lived there before managed.
Potentially bigger. There are a lot of old non-condenser boilers out there, with a typical efficiency of about 70%. And even condensers are often not much better than 75-80%; to hit the faceplate 90%+ efficiencies the system needs to be balanced such that the return temperature is in quite a narrow range.
Depends on the context; if you are presently using x kWh of electricity for non-heating plus 2x kWh of gas for heating, your options for electrical heating are either to 3x your electricity demand by "upgrading" to resistive, or 1.5x (or whatever) your demand by upgrading to a heatpump.
There's other stuff you can also do, but costs are all over the place, e.g. my 110 ish sqm house in Berlin is so well insulated (and has heat pump) that even while it's snowing outside it's hot enough indoors to be naked, for an electricity bill that's lower than that of my 37 square meter apartment in the UK, despite German electricity prices being much higher.
If your gas boiler were replaced with a heat pump with an average COP of 4 it would only require around 4,000kWh of electricity to provide the same amount of heating.
Electric cars are similarly 3-4x more efficient than petrol cars on a kWh of fuel basis.
So while we should expect increased electricity demand as transport and heating are electrified, the increase in electricity usage will be far less than the decrease in kWh of fuel.
Sadly for me my gas is 1/4 the rate of electricity so it would cost the same. Ironically it’s the gas marginal rate that keeps the electricity cost high.
Rolling the heat pump into the overnight battery calculation could work to offset the cost of install of the heat pump but I can’t stomach the thought of replacing my radiators and pipes.
Just to be picky… electricity…
We've still got a lot to do to decarbonise the rest of our energy usage EVs, heat pumps, improving housing stock, electric trains etc