Can household water be used on my garden

It seems like an awful lot of effort, filling your waterbutt with bath water, unless you live in a bungalow. I'm not being critical, but, why can't you fit your waterbutt to the downspout? There are various kits and diverters available for just that purpose.
Anyway, back to your question. I know of quite a few people including myself who have put waste water on the garden. Providing it contains nothing caustic or bleach, it should present no problems. The soap in the washing up water will help to repel greenfly.

I frequently use kitchen washing up water for my tubs and pots and have never had any problems.

Yup! Me too. I'm a great "chucker" of a bowl of COLD soapy water - not had an invalid yet!

I also use the water out of my fish tank - great fertiliser!!

Hi I have two waterbutts with adown pipe diverter easy to fit and a bit of soap doesnt hurt the plants.. I also use two old plastic dustbins and fill them with water from the sink especially when I start with cold to get hot water. the starter water(cold ) gets thrown on plants in plants or to fill the bins. I have even filled the bins with bath water put the lid on and it allows the soapy stuff to settle or get further diluted by other added water. so long as your water isnt greasy a little soap doesnt hurt the plants good for you saving water.