It's living on immoral earnings. That's what it used to be. Now it's called control for gain, and is applied in the same and similar circumstances. Usually directed at brothel owners, but a search will reveal that the police do prosecute partners if they feel so inclined. It's quite complicated, but basically if you live or co-habit with someone but not married they can be prosecuted. AFAIK It sometimes happens to housemates who have little or no knowledge of what is going on. Maximum sentence is I think seven years. If he can't show he is earning then he has little or no defence. Could be serious if you were investigated. I don't know what others will think, but I think it would probably be wise to get him to leave for that reason alone. You need to take advice for a definitive assessment of the risk. My guess is that it is illegal for you to give him any of your earnings or support him, and he could end up in jail as a result.
Living off immoral earnings was abolished in 2003. So unless a boyfriend/partner/husband that lives with you actually CONTROLS or COERCES they are fine. no helping with any aprt of the business and all is dandy. Lots of ladies live with partners.
OP-I think it is hard when we can earn a fair bit and yet are not working long hours. If a partner kept the house clean, shopped, dealt with all housey stuff, I'd be happy with them doing some work from home for 16hrs all things considered. Even something 'paltry' like ebaying.