Now I know that I have a good credit history as I have never used a credit card, always pay bills on time and I had a contract with Orange a couple of years ago which ended fine with no outstanding debt.
Stupid or not that's the way things are but there is really no need to be a victim. After all millions of people, some with dodgy credit ratings, have mobile contracts in spite of the apparent stupidity.
Some good advice already I would just add a narrower focus on what to do first. You say that you "know" you have a good credit history but the issue is not what you think but what your credit report says. Not any credit report but the report for the Credit Reference Agency which Orange searched. You need to ask Orange which one. They are obliged to tell you.
I can infer from your post that you probably do not recognise the importance of electoral registration for your current address otherwise you surely would have said. So, among other things, you should find out which CRA Orange searched and check that credit report for errors and omissions, in particular that your current address is recorded, there is an electoral roll registration for your current address and that your previous addresses are registered going back at least 3 years.
Not having a credit card by itself should not mean a poor credit history because current accounts should also be recorded. Unless you are also a current account refusenik.