A few things to check :
- that you are on an economy 7 tarriff so the night usage is at a much cheaper rate
- that the water heating system is on a timer and only on for an hour or so in the early morning ie. at the night time rate
- is your usage much lower now you've moved to summer usage (ie no heating)
- that the hot water tank has got some insulation and the rest of the falt is as insulated as possible (especially the windows)
For info I'm renting a 1 1/2 bed flat (one bed with bed deck) with no gas and used an average of 1 unit per day and about 4 night units over the period from mid April to end June. However, I'm not there at weekends and only three nights in the week and never use a washing machine. The only things on at night are the fridge, freezer (both not full so probably running inefficiently) and the water heating system but all of these are on 7 days a week. So your 12 night units seems high for summer usage but low for winter usage (ours averaged 18 units with the heating only being on 3 nights a week).
It might be worth checking you couldn't do better by changing suppliers based on your usage. The figure I've been quoted for two bed flats (based on normal full time occupancy) on more than one occassion is £50 - £60 a month average for the year.