mila -my dd has very sensitive skin too.
tbh the last thing I would use is Ecover (vey expensive, and didn't do that great a job, imo)
I used Ecoballs, or soda crystals.
I had 16 nappies for dd1. total cost (then) of about £150. Even as a newborn she never used more than 10 a day - wash at night (usually with her other bits and bobs - muslins, clothes if leaked on - stuff that would have been washed anyway, iyswim), hang out (no tumbling here) on an airer in bathroom next to open window, bobs your uncle.
since dd1 was still in nappies when dd2 came along, I had to get some more. another 10 (pre-owned this time; a mix of small for dd2, and toddler+ for dd1). another £40 or so.
negligible detergent costs (ecoballs are a one-off outlay).
and once past the newborn bit, I was using more like 4 a day - so washed about every third day.
by your costing of 50p a load (really? I'm not sure it was this much, but haven't really researched this) that's about £1.50/week.
so, all in for £250 or so for the first year with dd1. and much reduced (obviously, ince I didn't have to buy nappies) for the following 2 years - washing costs estimated at £78/year, going by your figures.
then, another £40 when dd2 came along, for more nappies. and still running costs of £78/year.
overall (I did use reusable wipes - old bits of facecloth, old tea towels etc, so no extra cost), for the 5 years I had my 2 in nappies, costs were:
drum role........
£602.
for 5 years worth of real nappy use. add on a few extras, if you want - I am sure I must have used some detergent over that time, and maybe even the odd emergency tumble dry.
going by the current cost of disposables, I would have spent considerably more if I hadn't used cloth nappies.
and then the nappies were used by my SIL for 2.5 years, for DN - again, she uses ecoballs, so a running cost to her of £78/year.
and the nappies are back and awaiting dc3 here (or dc2 for SIL).
there is no way you can compare these totals to using disposables. no way at all.