Unfortunately for you (and, I would argue, everyone) .6 FTE teaching-only contracts in the UK are, by and large, used by the Universities to squeeze out as much work for as little pay possible. They are often conceived of as a way to mop up the teaching and admin tasks that researchers with full time research+teaching contracts don't want to do, perhaps because one of them got a big grant which buys them out of teaching and admin. Thus the answer to your question is that you likely have to do a lot of admin and you likely have little choice about it if you wish to keep your job. Indeed many of these .6 FTE positions are on rolling contracts so they can let you go if you aren't performing. As for what admin you should do and what you can say no to, that is something to discuss with your line manager and your head of school. you should have some sort of work load model (or equivalent) that helps spell out what your duties are and then helps you say no to things that are not your job. It is very possible that people are piling work on you because, again, you are in this position that may have been created for work to be piled on to, but it is your line manager and head of school's job to make sure that you aren't doing too much. If they are the ones giving you the work, well, you should probably be looking for a new job.
A note on .6 fte teaching contracts because what you said above is a common but distressing sentiment. You wish to advance your career and gain promotion on the back of your research which you say you do in your unpaid time (though, of course, your Uni gets credit for). However, as you are on a teaching contract, you will be evaluated for promotion based on criteria related to teaching; it is very rare for someone to have their position regraded from teaching, and I've never actually seen it happen. It sounds to me that you are in the wrong position; the position you are in does not match your career goals and is very unlikely to lead you to the research career you are looking for.
Finally, though there is variation, "senior lecturer" is a title that everyone has at UK universities irrespective of if the are "teaching" or "research and teaching". I'm a senior lecturer, I'm on a R&T contract, and 75% of my time is pure research, with 25% of my time for teaching, supervision, and admin. You sound like you DO want to be a senior lecturer, just that you want to be in a full time, traditional, research and teaching role.