I've only worked in small firms but I would say that in general they would be a little put off by someone with an LLM. They wouldn't consider it to be really relevant to practice and would worry that you were academically inclined, which may not sit well with general practice life. You may of course be aiming for the bigger firms and I can't really answer for them. The difficulty is at the moment that if you only aim for the big firms it limits your options considerably, as you probably know by now.
If you don't have significant work experience to date then I'd say you'd be far better off getting that. Any kind of work in a law firm, bank, insurance or similar place might be more beneficial if your aim is to get an apprenticeship (any apprenticeship!). Or if you haven't done it you could go travelling for a year. Any partner I know would consider that a perfectly normal thing to do, especially in the downturn we're in now. Provided of course you get decent work experience out there. It doesn't apply to all, but many partners in small or medium general practices have a bit of an anti-academics bias. They might be a bit prejudiced that somebody with too many qualifications would be seriously bored being an apprentice. Especially when they have so many applications to choose from.