I was openly honest with my previous employment. I took days off no different from anyone taking annual leaves and took time in lieu for phone interviews between working hours. Unless you're in some kind of job where you actually can trump them by holding your cards close to your chest, just be open.
It's company's responsibility to induce loyalty from employee, not demand. If your current company isn't doing that, you're more than entitled to look for employment else where, so long as you keep your current responsibility checked and obviously not divulging any company secrets if potential new employer is a direct competitor.
Which surprisingly I'm also supposed to be working on that day and the following day I'm off for nearly two weeks.
