Tariffs vary but averaged across the country, under the current OFGEM price caps, electricity costs four times gas per kWh. This means that by my estimate [1] unless you go off gas completely (hence avoiding the fixed daily charge) you need a heat pump efficiency (SCOP) of 360% to get similar costs. This is not unknown but considerably better than average. If you do go off gas completely, you need 320% which is still better than average. If you only got 300% you would be paying 6% more with the heat pump than gas. This is discouraging for people wanting to switch to low carbon heating.
However, a significant part of the electricity bill is due to environmental and social policies or 'taxes'. If these were removed or shifted, the ratio of electricity to gas price would be smaller, making heat pumps relatively cheaper. Hitherto, policy has been to keep gas cheap because so many of us rely on it for heating which is essential for health. However, doing so penalises households that make the transition to low carbon heating. What are these taxes and how much difference would this make? Here is a graph showing policy costs on gas and electricity as of September. There are more policy costs on the electricity bill than the gas bill and the home with a heat pump uses more electricity, so pays even more policy costs.