To put up a bloody great big fence?

[Elemis]

neighbour over the back has decided to cut down a lovely bush. They can now see directly into our garden. Directly into the house even. I have no idea why they have done this. They haven't cut down the horrible blackberry bush that overhangs into our garden, or tidied anything else.
Can we just put a fence up? Any problem with that?

You can do what you like provided the fence is within your property.