One thing you can do is to plant bushes of any height you like, 12 foot laylandii are perfectly legal, a 4ft fence isn't.
I know how you feel as i went through similar thing myself. We wanted to put a fence up to make a part of our back garden private and secure for Siobhan to play in. The fence would only be 4'6 high but as our garden is raised by 18" it would make it 6 foot from the pavement. In the end I did get permission for a fence but it had to be 2 metres back from the pavement. The daft bit is that they said I could have a 6' fence there so now its over 7 foot high from the pavement! The 2 meter gap I filled with chippings which one of the neighbours is complaining about as the odd kid that walks past our house tend to pick a few up and chuck them at his window
I swear that our planning dept are thick as two short ones. Thsi was the second incident I had with them
One question though, have you thought of asking the RSPCA to come and inspect your garden? IIRC they will advise if it isn't secure enough for your dog so you could actually get a report from them saying that you NEED that fence to comply with the legal aspect of owning your dog.