If I get refused because rent is not enough, then it's plain stupid.
How is it stupid that they require you be able to support yourselves?!

If you aren't contributing enough to the rent/utilities, they will notice as they've cracked down on third-party financial support. You'll need to be as detailed as you can with your budget:
Rent (should be reasonable)
Insurance (contents insurance, car insurance, etc.)
Council Tax (if this is included in the rent, again, it should be reasonable and reflect that)
Utilities (if this is included in the rent, again, it should be reasonable and reflect that)
Telephone (landline? contract mobiles? PAYG?)
TV license (if this is included in the rent, again, it should be reasonable and reflect that)
Health (non-BC medications aren't free, contacts/glasses, etc.)
Loans (or any other type of monthly bill)
Transportation (petrol, bus/train/metro passes, cab fares, car payments, taxes, & maintenance, etc.)
Food (£40-50/week is probably reasonable for 2 people)
Entertainment/pets/misc