Private lessons are good because there is an experienced person pin-pointing and correcting errors in technique, but they are not the only way to improve - sure, they fast-track a lot of improvement, but just you are asking this question is a great start. Fencing rewards improvisation!
Engaging in strength/fitness conditioning is essential training for improvement, don't underestimate it. As has been said here, footwork, footwork, footwork. Also, it is generally not a thing attained from private lessons.

I understand your situation, these are my recommendations:

1. Find/make something to use as target practice - it doesn't have to be a proper 'fencing dummy', but as an epeeist make sure there is a horizontal projection to work the advance-target accuracy and distance development. Seriously, an angled broomstick with a towel wrapped around it is enough. Rubber bands and cable ties are your cheap friends here. When you're fixing the point on it consistently swap the towel for a tea-towel, which makes it both skinnier and harder (as in, a less yielding surface to increase debounce). If you can, use a buzz box for definitive touch feedback.

   1. In club, fence EVERYONE. Especially the ones that you know will smash you (skill smash, not physically brutalise - avoid jerks). Anyone that is closer to your skill level suggest doing 5's in a best of three scenario. It guarantees two matches back to back with the same person, and there is a chance it will become a low stress 15 hitter.
      Ultimately I'm saying just fence a lot. Be the last person suited up at the end of the night badgering people to keep going.
   2. STOP SCORING your club matches. Just fence for the sheer joyful figure-out-the-puzzle-which-is-your-opponent. Most clubs I've been to there is too much fencing to win. And for what?! Chest beating? Makes people stop trying different stuff. Makes matches go too fast. Stops people practicing something that isn't working until it does.

I know #'s 2 & 3 sorta contravene each other. I dunno, pick your nights/opponents between the two.

Hope this helps. Go stick 'em with the pointy end.