"Inclined to" can mean a small preference toward one particular option, or it can be a more polite way of expressing a choice or preference. Examples: John and Samantha, your two close friends, are arguing in front of you. They stop and ask which of them you think is right. Because you don't want to hurt John's feelings, you could say, "I'm inclined to agree with Samantha." A friend invites you over for dinner and gives you a choice between two dishes that both sound equally delicious, a chicken and a beef dish. You could say, "They both sound great, but I'm inclined to choose the beef dish."

"To be inclined to" means have a tendency, preference or disposition to do something. Your example is in present perfect. "I've been inclined to ignore criticism of my English". (That was the tendency).