Make a spreadsheet or list of where it all goes. Before you can figure out how to stop going over budget you need to know where the money is going, so set it out like this:
a. rent/mortgage £x
b. council tax £x
c. gas, electricity, water, phones, net, tv, insurance £x
d. food £x
e. debt management and stuff bought on credit £x
f. petrol, taxis, public transport £x
g. clothes
h. subscriptions (magazines, games etc)
i. luxuries (takeouts, nights out, gifts, etc)
j. anything else
Then add it all up. If it's more than your average monthly income, you're overspending. If it's less, but you're still short every month, you're spending more money than you think, and you need to start recording every penny you spend for a month or two until you figure out where it's going.
Once you know that, you can decide how to work with it. My DP and I have a joint account that we both automatically have our half of the rent and 'unavoidable' bills (water, electricity, council tax, phone, internet) go into on the day we get paid. That ensures there is always enough money to pay those and we don't end up in arrears. As your partner's income isn't regular, this might be less easy for you, but it's worth considering.
Then everything else - set a budget and stick to it. If you are overspending, try and take a hard look at what you are spending the money on and if any of it can go. Cheaper deals on utilities, insurance etc are always worth investigating. So is canceling something you don't really need - what you do and don't need is specific to you, of course, but I'd suggest tv packages (freeview works fine), 'luxury' foods (ie don't buy pre packaged smoothies, either drink water or make your own from fruit), shopping in 'expensive' supermarkets (when broke I buy most of my shopping in Aldi with topups for stuff they don't have in Morrisons or Tesco), and things like that.
Might it also help to space your bills out over the course of the month, if your partner's income trickles in in bits, rather than at once on payday? Just so they don't all hit at once while you're really broke? I've often found companies are quite willing to change the date on a direct debit if you ask nicely.
Hope you get to the bottom of it, it's awful not knowing what you're doing wrong isn't it:( Been there, done that, so have much sympathy!