I was in a similar situation (passport expiring before Visa). I had the option to transfer my Visa to my new passport (for an additional charge, of course), but instead I simply renewed my passport and continued brining along my expired passport containing my (still valid) Visa whenever I travelled out of the country. Never had a problem. Eventually, a customs official at Heathrow put a stamp in my new passport that explained the details of my current Visa status - it said little more than the fact that I was permitted to enter the
UK until (Visa expiry date), but I've since travelled using only my new passport with this stamp. Again, no problems whatsoever.
I'm not certain what the official policy is for situations such as these, but just thought I'd share my experience.
Hope this helps!
- C