This got me wondering, so I did some checking into it. Landlords cannot gain access to any of the account data on your credit file. The "credit checks" that the agencies perform are based solely on public information, that is: details of CCJs, bankruptcies and voluntary arrangements.
They can't see any of the account info on your credit report (the bits that say "3 payments behind on a credit card" or "defaulted on a loan"). Furthermore, any credit score given by any of the agencies does not take into account any of that info, because the agencies cannot even see that info, so there is no way they can base their score on it.
Experian offer a tenant verification service, and even their report does not use the account info. What they will do is use their records for identity and address checking, but the actual credit info is strictly off limits.
So, to answer your question, missspeedy23, unless you have been declared bankrupt, have entered into a voluntary arrangement or have CCJs, none of your adverse credit will be visible in the search.