Unfortunately, because of the type of aid that I'm getting, it's more black and white :( There are different kinds of aid where it's possible to do as you described and they basically deduct any earnings you might receive from whatever they give you after you've reported them. But yeah, the type that I'm on doesn't allow for any kind of income whatsoever before you get booted off >.< When I spoke to the people at Citizen's Advice, they said another option would be to move to the more flexible kind of aid, but there was quite a big catch, that you have to actively look for work and prove that you're doing so/that you've spent at least X hours per week looking, and you must not turn down any interviews/job offers, etc. or they will take the aid away immediately. Because of how crap my mental health is though, I likely wouldn't be capable of doing everything required, and wind up losing the aid.
The biggest problem though I guess is their lack of willingness to understand that not all money you receive is necessarily income. For example, at Citizen's Advice they told me, if your grandma gives you £10 for your birthday in a card, you're technically supposed to report that to them so they can deduct that £10 from your aid. So they basically said that even if I were to make the switch, they wouldn't understand/care about any costs involved in game dev like fees or fundraising in bulk, they just see anything at all coming in as income to be deducted from what they give you >.<
The system is supposed to be changing though. So all I can do is wait and see what happens I guess.