In 2013 I completed LEL with no experience of 600, my preparation only included one 400, one 300 and several 200. It's been the hardest experience of my life, so far, and I wouldn't suggest to repeat it. After that, I completed several long randonnees, including PBP 2015, far more easily because I had gained experience from LEL and prepared better.
Going back to 2013: there was no 600 at hand, close to my hometown; I was very busy on a new job; I had completed the 400 quite easily not sleeping at all through the night, so I decided to skip the 600 lesson. During the late spring and summer, I went on training on long, single days. It was not enough, as I understood later. Shortly before leaving for the UK (I live in Italy) I grew more and more afraid, as I felt I was underprepared. When it came to packing, I was so scared that I took all my summer and winter clothes, also the gloves I use when temperature falls below 0 Celsius... At the start, I guess I was carrying the heaviest luggage, plus two overstuffed drop bags that the volunteers were so kind to accept even if they were really exaggerated. Everything went fine on the first two days. Problems began shortly after Edinburgh: my ankles started hurting, then Shermer's neck began on the way down from Yad Moss, while hands and feet were growing increasingly numb and tingling, only to mention the main issues. Three days of real pain. After arriving, it took me a couple of days to recover, except for my tingling hands that improved slowly and fully recovered only after more than a month (ulnar nerve, as I came to know later).
I didn't give up only because my mind controlled my body: my wife and daughters were waiting for me at the arrival, I had talked to all my friends and acquaintances about the great adventure and I didn't want to lose face.
If there's no official 600 that fits your schedule, I suggest you to try with something else that keeps you on the saddle for at least two long days, three is better. In continental Europe there are several Super Randonnees, permanent, as described here:
http://www.audax-club-parisien.com/EN/421%20-%20General%20Super%20Randonn%C3%A9e.htmlNone of them are in the British Isles, but there's one in Germany, and many in France. I tried one down here in Italy, and am looking forward to using some of them for training this summer.
I fully agree with what previously said by others, that it's not just about training your legs' muscles, every part of your body must adapt to the experience of riding your bicycle continously for so long, and there's much more: you test your equipment, feeding, hygiene, etc. You gradually grow more self-confident, more at ease, and this too can help.