Make sure you have the latest drivers for the UAD1, and make sure you have Logic 4.81, which has a special setting for this problem. Go to Audio - Audio Preferences, and at the bottom of the page, checkmark the Plug-In Delay Compensation and hit Close.

If this doesn't help, try starting a new song without loading your autoload by holding CTRL while clicking File-New. Also try trashing your preferences by searching your Windows directory for a file called LOGIC32.PRF. Simply delete this file and restart Logic. Between these three suggestions, your latency issue should be resolved.