I'd like the "today", "yesterday", etc. links in recent activity to display in the user's current time zone, as well as any non-relative timestamps (for example, the absolute timestamp seen when hovering over a relative timestamp). It is annoying that the evening is a different day than the afternoon (for me on east coast US). I imagine for someone even further from London it's much more annoying.
You'd just need to add a time zone preference for users, and default it to UTC.
As for server-side things like daily rep cap, I don't think many users would care if those were still based on UTC.