Try again and take your report to prove you've got good credit history.
This would likely leave another credit check footprint though..... you may not want that

There are lots of different criteria that a telco may for their credit check to be passed, no telco will tell you exactly what the problem is - unless its something obvious like an unpaid default. Things like long tenure in jobs and homes help - show stability etc, too many credit check footprints can indicate that a person is credit shopping (and potentially getting knocked back by lots of creditors, so they can then be viewed as a credit risk. If it is a smaller telco, they may have tighter guidelines as they dont have the profit margins to take risk on potential bad debt, its just business so dont take it personally