So long as gas remains cheaper than electricity, it will obviously be ('everything else being equal') cheaper to boil a given volume of water with gas than to boil the same volume of water with electricity.
Not so sure, daughter boiled water in kettle and then poured it into the pan, and I asked why, gas hob around 5.5 kW and kettle 2.8 kW so she did a demo filled kettle to full mark, poured into pan, refilled to full mark and set both to boil at the same time, and the kettle boiled in around half the time for gas even when kettle was around half the size of gas ring.
I was surprised at the result, so when I got home repeated the experiment with an induction hob and kettle, 3 kW for hob and again 2.8 kW for kettle, the kettle won, but only by a very small margin, near enough same time.
In both case the lids were on the pan.
So since it takes around 4 times the gas to do same work as electric, plus it heats the kitchen more, and puts moisture in the kitchen, so need to run a cooker hob to remove heat and moisture. Even when gas is much cheaper to cook with gas likely around the same cost.
However for a gas central heating boiler (heater as we hope it does not boil) with the combustion air taken from outside, and the combustion gases exhausted to outside, it must be many times cheaper to heat home with gas than electric, as to oil with price raises not sure any more, it was cheaper to heat with oil to gas, but this may no longer be true.
My wife many years ago early 80's looked at gas cookers, she was looking at a Cannon with a built in microwave, around £1000 and this was in the 80's, however she looked at the fingers holding the pans, and decided it was too easy for our small children to reach up for a pan and cause it to topple off the cooker, I sighed a sigh of relief when she went for a ceramic hob cooker instead at ¼ the price, it has since been replaced with an induction version, and the safety features means no way would I use a gas hob on a cooker today, and as far as oven goes electric has more control, not sure if any point in the extra control, closed door grilling is good, but Mrs Beeton's has clearly been re-written, as no instructions as to how to set dampers with solid fuel cooker, which would have heated oven from bottom, side, top depending on settings, and it has a reference to gas marks and gas cooking was not invented until after Mrs Beeton. So oven has all the fancy controls, but I don't know how to use them.
Today the idea of cooking on gas and getting the gas bottles to power it does not seem a reasonable option, I know you can get oil fired ranges, but I think electric is best option when no town gas on tap.