I am an IxD graduate student currently doing an internship as a UX designer. I can't speak to the culture in the UK, but in the US, it seems like a lot of people with an ID background are getting into UX jobs pretty easily due to the high volume of jobs in that field, a potentially similar design process and good visual communication skills.
In my experience, my firm's deliverables are largely report books that aren't terribly different from an ID process book, so I think your existing portfolio might be a good place to start. I think inclusion of some kind of user research, a visualization of that and something that says/shows how that research led you to a next step is also important. I once heard a piece of advice regarding designs for ID professionals business cards "I don't care what it looks like as long as it's not terrible". in a different context, this is about the same thing I've heard from UX hiring staff regarding portfolios. They really just want to know that you can think. Good visual design skills are a bonus, UX folk love "unicorns" - multidisciplinary people, but I don't see people getting UX jobs based purely on visuals.
As for tools, I think the UX workflow is a little more open. Hand sketch is king because it's fast, and most things are just rectangles anyway. I do some UI elements in Illustrator. Wireframe tools are abundant. I most recently used Balsamiq for really simple screens, but have also used Axure which can model interactions a little better. there are many others. if anything, this is the only tool that an institution may have an affinity for a specific product. There's a lot of chatter on the conference circuit about nixing the wireframe step altogether and just building prototypes in something that outputs HTML/CSS... but thats a can of worms.
Overall, I'd suggest you find some local UX professional organizations and attend meetings. It will help you get caught up on the vocabulary and hot topics. usually groups also give workshops and the like. IxDA has chapters all over the world, meetup.com is another good resource.
I know very little about service design in industry at this point. I'm planning to do my thesis on it, and have been doing some learning. it's not as big in the US as it is where you are. I get the feeling that in the US it is more closely attached to marketing departments and the Customer Experience idea.
Hope thats helpful. if you ever want to chat about this stuff in more depth, let me know. I'd be interested to hear your experiences working at a firm that has some contact with these fields.