Davros, as a general rule, the mob won't release information like that, unless it is a high-profile visit. Seeing as Pompey has ships going in and out as routine, you'll be very lucky. My advice is to check the RN website, and keep half an eye on the local press. Navy News also publishes ship movements, but normally only after they have happened and in broad terms.
I can understand how it's not ideal for enthusiasts, but the security situation makes it very risky to reveal too much.
Friday afternoons are always the best time to get to the Round Tower or wherever you like to spot from, with ships retutning from Thursday War and other training for the weekend.
Also, having checked out the link provided by Kato, i would suggest that you don't rely on it too much! They're quite variable, especially with smaller vessels like the Archer-class they've listed there, and it all seems to be ''community edited'' (or whatever the term is). Make sure you're watching out tomorrow afternoon/tuesday morning (i'm not sure which), and you'll see that they've made quite a significant omission from that list!