If your blood pressure is normal, you should not have a problem walking. If this is something new for you, then you should ask your doctor about. Always ask before beginning any exercise program especially if you never did it before. The first number may go up slightly as you walk but the bottom number should stay the same. Generally, the faster the heart rate the higher the first number will be during exercise.
What if the bottom number goes up? I was walking around in wal-mart the other night and took it on their machine (I hate those things) and it went up to around 100. I know I shouldn't trust those but there wasn't anything else around.
As Rick mentioned, during dynamic exercise, the systolic rate should rise steadily as the intensity of the exercise increases, while the diastolic rate should change very little. ...
A good rule of thumb is...If the diastolic rate increases by 20 above the resting value, or reaches 120 or above, then exercise should be stopped. But your doctor may feel a different "threshold" number is okay for you.
What is your resting diastolic when you monitor it at home?
High blood pressure does its damage by being high for YEARS and YEARS. THus, an exercise peak is absolutely nothing to get concerned about, in fact, it's probably quite desirable (pet theory.)
Worry only about a resting BP that is high day in and day out, week in and week out...for decades!