Quoting Sally1984
Should we see both the north and south island?
What sites to see and do?
How to travel around fairly cheaply?
Is a month long enough?
If anyone has a common itinerary that would help as we are pretty clueless at the moment.
I don't currently have the time to draw up a complete itinerary, but here's a three week one I wrote a couple of months ago which should serve as a rough basis for what to see and where to go. With the extra time you have available, I'd add on a trip up to the Bay of Islands and Cape Reinga immediately after departing Auckland, then visit Cathedral Cove on the Coromandel Peninsula, plus just generally pad your stay in most places on that itinerary with an extra day.
A month is never "enough" time to see New Zealand (if you can easily add on more time, the country can easily accommodate it; there's always more to see, and to see in more depth), but it is enough to give you a decent overview without feeling you've missed anything absolutely essential, and yes, does allow you to see something of each island.
Given that you're going in September, which is low season, the cheapest way to travel around is almost certain to rent a car (or optionally a campervan, though personally I'd consider that too cold in many places) and stay in hostels (which frequently run "stay two nights, get the third free" that time of year).
Also we are on a budget, looking at around £1000 each for a month, including accommodation and transport. I would alos like to do a sky dive, and white water rafting possibly...
£1000 currently works out to $2600 (this has been fluctuating rather heavily this last year, so be prepared for a change of up to 10% in either direction), which would give you a budget of $85 per person per day, or $170 total per day. Figure $50 per day for car rental including gas, ~$55 per day for a double room (more expensive in the big cities, but also significantly cheaper in smaller hostels in in between places), $25 per day for basic supermarket food (cooking your own meals in the hostels) and $10 for incidentals. That leaves you $25 per day, or $900 total ($450 per person) for activities like skydiving and rafting. It's a bit tight, but certainly doable. Just keep a careful eye on how much you're actually spending, and maybe consider saving some money every so often by staying in a dorm room or eating pasta. 
Enjoy your trip; you'll be going to some awesome places! 