Hi Ben,
I used to work in debt recovery, so I may be able to help a little. Firstly, in answer to your question, notices of default do not have to be sent special/recorded delivery. But if indeed this was a ligitimate debt, it would automatically be be referred to a collection agency.
I think you are taking the right approach to this, but my tack would be to get a little more aggressive in my letters - tell them that you will give the (a very fair) fourteen days to either produce evidence that the debt was owed and letters sent (to the correct address), or you will issue legal proceedings against them and refer the case to the relevant governing body. It is no hardship for them to ammend your credit file, it only takes one e-mail/fax to the credit reference agencies. And remember, if you call them, make sure you get the operator's name and make notes of the conversation. If you write, (a white lie), write 'copy sent to solicitor'. They won't want litigation.
One other thing I would suggest is to get your credit files from Experian, Equifax and Call Credit and add a 'notice of correction' to your file while they are sorting this out. If you do owe this money it may be difficult to argue that you didn't receive the bills, but the fact you had a direct debit with them will help. At the end of the day, if you owed them, they would of just taken it from your bank. Either way, lenders looking at your application will take this notice into account when making a decision.
Though I must admit to being a happy T-Mobile customer, I don't like how easy it is for company's to screw up your financial 'life'. This happened to my old mum with an unjust bill from British Gas which we managed to fight. So don't give up!
I hope this helps.
Rob