I'm working on my UCL application now, and they state a character limit of 3000 for the main textbox for the personal statement. But they also state that if you exceed that, you can attach the full personal statement as a separate document. I take that to mean that there's no word limit?

Also, does UCL do rolling applications throughout the application period?

yes that shall imply that there is no word limit but it should be concise. writing a long statement can cause more harm than good.

I was informed via telephone that 1,200 words is still within limits. Not sure how much higher you can go, though.

I think I submitted mine with about 900 or so. Now's just the waiting!

You should try to write short and perfectly. Around one-thousand words would be enough.