When to go
Best time
Morning, Mid-day, Late afternoon
Since it's an interior shot, you can photograph St Paul's Cathedral during any month of the year.
Visit during the day, although you are mostly relying on internal lighting. It can help, though, to have sunlight entering the space from the high clerestory windows above. St Paul's Cathedral is generally pretty dark inside so any daylight entering the space can be of benefit!
Field tips
Tripods aren't allowed to be used inside, but they have very recently allowed photography for your own private use.
Use a wide-angle lens (10mm) to incorporate as much of the choir hall and ceiling as you can. Take multiple wide-angle photos from low to high perspectives and combine them using computer software (like Photoshop) for a panoramic photo similar to this one.
For a perfectly symmetrical shot, position yourself right in the middle of the building with the lectern in the center of your frame.
You may need to raise your ISO to ensure your shutter speed is quick enough for sharp pictures.