Well said sessidesally.
OP, I suspect that your neighbour has a different view of life to yourself, and does indeed look upon our garden as "hers" - not in the legal sense but in the sense that she obviously enjoys looking at it and feels proprietorial towards it. She probably doesn't "do" change and may feel a little threatened by it. The building works may have increased this feeling.
Legally, of course, you are completely in the right and there is no reason on earth why (subject to complying with planning law etc.) you shouldn't do what you want in your own garden.
However, she is your neighbour. It may therefore be worth humouring her a little - just grin and bear it and say something along the lines of "yes they were nice but they had to go as we wanted to put our shed there" etc. You don't need to concede anything and do be firm that it's your garden but perhaps acknowledge her feelings?
Dealing with her assertion you should have consulted is a bit trickier as you don't want to get into a position in which you feel you have to ask for her "permission" to do something, when you don't. Perhaps side-step it, and say something like "It was tricky working out where we could put the shed, and we thought long and hard about it but decided this was the best option." If she pushes, you may have to just firmly say "It is our garden and we thought..."
Personally, it would bug me too. Previous owners of my old house were informed by neighbours I was uprooting their (I mean formerly their) conifers....and they turned up to liberate them before I tossed them in the skip. Very weird, especially as they had planted them about a foot away from the house and I had to "explain" that nice as they were (I lied) I wanted to keep my foundations.
People are very weird about "their" property though and I have seen enough boundary disputes to bite my tongue on occasion.