If DP is willing to work evenings/nights and weekends - great for childcare sharing so long as the other partner does not have to go away with work -
then can suggest :
retail, warehouse packing, night care, hospital portering/night reception, hotel night reception, security, bar work, out of hours cleaning, piece work - curtains/blinds/knitting machine etc
all minimum wage or thereabouts - though NHS and councils have a tendency now to pay "living wage" which takes you up a pound an hour...
As a tutor, I found students by putting an ad in the local magazines - including the church parish magazine (I don't go to church, but they will take the heathens silver...) - then after I got 2 or 3, word of mouth took over. Rates round here are between £20 and £30 per hour - but really half that if you include the prep and marking time.
The kids piano teacher just puts his ad in the parish mag. £25 an hour - he comes to us.
Only thing you have to do is contact the tax man and say you are self employed, and get insurance (not expensive or hard to find). I give jewellery making courses at the local tech too sometimes - any local adult education colleges recruit between now and summer usually... get their name in there.. wages around £12-£15 an hour for that - BUT it ends up about minimum wage when you take into account preparation hours too.