Question: How much contact should I expect to have with my literary agent (from a sizeable London firm, representing my first novel)? Are months of silence to be expected/endured? If so...how many?

Answer: 
I wasn't going to post an answer for this, but I've got to disagree with Joshin. 

You're in a business relationship with your agent. You're entitled to respectful business communication. There's a vast difference between you needing your hand held and you needing to know what your business partner is up to.

Months of silence seem out of line. That is, if you've sent a polite, business-like inquiry, you should have been answered. If you've been nagging him/her daily, then maybe s/he has shut down. But you haven't said anything to suggest that.

Rather than Joshin's manufacturer/salesperson analogy, I would try home owner/real estate agent. (You notice the word 'agent' - it has significance). If you allow someone else to try to sell your valuable, unique property, you are entitled to regular updates as to their progress. If you've been reasonable, and they refuse to share this information with you, there's a serious problem with the relationship.

There are a lot of great agents out there, and there are, unfortunately, a lot of rookies and/or shysters. If you have absolute confidence (through checking at Editors & Preditors and other relevant sites) that you've got a great agent, you might want to forgive the poor communication. But if you're less than confident, you need communication to know what's going on.
If you are really good they'll be happy if you just send them a check on a regular basis. 

Think of a clerk in a store. Their job is to make sure that when a buyer comes into the store they find what they need. Rarely (if ever) do they contact the guy in China who is making the tools. 

If you are making tools in China you want the clerk to sell them in the US of A. 

If you need hand-holding use part of your royalties to hire someone with hands you like.