The minimum for working tax credits is 16 hours, I'm not sure about UC.
Housing benefit calculates your wages and benefits as income when they decide your award amount.
Every pound over a certain amount they will put your HB down and for some people it isn't worth it. Finding childcare, paying for another commute and then actually working the hours out for a few extra quid might not be worth it for some people.
Picking up a few extra hours here and there and you will have HB change your award notice and calculate it at the highest that you earned.
For example, at one point I had a zero hours contract and dispite me telling them by email and phone that my hours will fluctuate (and we agreed for me to send mybpayslips every 6 weeks to calculate HB), they would change my HB if I recieved more wages one week.
Even if the week after I recieved nothing they will say from now on your HB is £60 for example. I would then have to chase them to change it and go into rent arrears. They also conveniently wouldn't change the award notice when my hours were less. And you would be on the phone chasing emails that you sent and having council workers say they didn't recieve xyz.
I had to write to my MP at one point as they calculated a week I earn £350 as me earning that every week and then didn't respond to my emails or phone calls that that was one weeks and not the average in a week of 6. They also claimed that they then overplayed me HB and I would have to pay it back. It wasn't worth it.