Unlike the OP, my immersion element is top entry in to the hot water tank, so it can only heat the top half of the water content.
This makes the relative cost calculation more complex. With my Eddi I have a choice to use electric to heat just the top half of the tank which is sufficient for 2 quick showers and a bit of washing up and uses around 2-2.5 kWh per day depending on the residual heat from the previous day.
Typically once a week SWMBO prefers a bath, so the gas boiler is activated which heats the full volume of the tank and uses around 7 kWh (from meter readings taken last summer just for heating the tank).
The standing losses from the tank will be higher when the whole tank is heated rather than just the top, even with the extra insulation I have fastened around the tank.
My cost comparison then is:-
1/ Electric = 2.5 x 16.6p (Eco7) = 41.5p/day worst case with no solar top up for 6 days of the week.
2/ Gas = 7 x 10.25p = 71.75p/day on bath day, or every day if electric immersion not used.
Some people may use the full tank every day, so the comparison becomes different, as well as with different tariffs for elec vs gas.
I also use the 2nd output from my Eddi to power 2 oil filled radiators, that help out the gas boiler heating in 2 regularly occupied rooms on sunny but cold days, so it is not just about what you can do with the immersion.