Having gone through a similar phase with my son, I know (as with all these things) that it will pass with time. With my daughter however, it is a little more full-on for me as a parent, as she is mostly affected during the day and whilst awake. She is fine once in bed asleep. I literally can not leave her to play for a few minutes while I am cooking dinner or getting the baby ready for bed. Sometimes she is ok if her older brother is with her, but more often than not, only mummy will do.
I am trying to remain patient and understanding. It is a little wearing but I am aware that she needs reassurance and plenty of love and respect for her feelings while she is going through this stage. It is the flip side of a preschooler's independence, whilst happy to go off and do their own thing at times, they can then get worried that mum or dad will go off and leave them. If I tell my daughter I'm going to do something like change the baby's nappy, she'll say, "and then you'll come right back?". Of course, she will follow me anyway....
One day she might not want to come anywhere near me, or be in the same room as me! So for now, I'll try to enjoy the closeness and cuddles as much as I can.
Can you remember your preschooler going through a similar phase? Was there anything you think helped them get through it or was it just a matter of time and patience?