Nothing particularily unusual about your situation but it is quite possible to reduce the noise by getting 'low noise' tubes (assuming that you don't have them, or that you present ones are worn out). They cost more but are worth it.
BTW, tube phono sections are often noiser than line stages, and matching the output of a cartridge and the output of a phono stage can make a difference, especially if you are using a low output MC cartridge.
You don't mention your other components but some tube pre-amps have high output and when coupled with amps with high sensitivity and with speakers of high efficiency you will have a hard time correcting pre-amp tube noise without some specific effort.