I did it for a while and the answer is.....very little.
Weekend days are prime time at flying schools and are generally fully booked. You might do 5 hours a day but if they're paying £15/hour, you'll only gross £75. In my experience, schools are rarely fully booked during the week, so you might average 3 hours on a weekday - or gross £45. Even at £20/hour, we're talking £100 and £60. However, without a retainer, you'll learn nothing on a bad weather day. 5 hours a day assumes 5 PPL students. 5 half hour trial flights = 2.5 hours flying = poverty.
The big commercial schools are a different matter, generally more flying and more pay, but fewer opportunities for part-timers.
So if you work 8 days per month and 2 are weathered off, so you work 3 weekdays and 3 weekend days, you might gross £360-£480. If it's winter and 4 are weathered off, you might gross £240-£320. From experience, even these figures seem high and I would reduce them a bit due all the variables such as tech aircraft, "no show" bookings, etc.