If you are using flat rate electricity at the price gap, no, it will cost roughly the same to run because electricity costs 4X gas.
However if you use a time of use tariff or solar or solar and batteries you can save money, potentially a material amount of you have all 3.
I can push between 30% and 45% of my demand off peak in winter at 7p/kwh 23:30 and 05:30.
Take today for example, it’s a cold day, my heat pump used 26.8kwh, 10.3kWh of that was between 00:00 and 05:30 at 7p/kwh (38.4%) costing 72p.
The rest in theory cost £4.45 but that’s before you factor in solar and batteries, I generated 6.6kwh today and I’ve got a 13.5kwh battery which I also charged at 7p.
In total I used 39.2kwh for everything but only 32.6kwh was from the grid. 6.85kwh was at 27p, 25.75kwh was at 7p so my bill for today was £3.65 or 11.1p/kwh.