You can, but only with the agreement of the head, which is not often forthcoming from what I have heard.
Here
The way most people I know get round it is by registering their DC as nomadic which gives you the freedom to take them out for extended periods without notice, and to enrol them in other schools/areas on a temporary basis. But this requires you to show a clear commitment to a travelling lifestyle as a way of life, not a hobby, and some LEAs are very strict about how they interpret this.
Can you not fully HE until you find a school you are happy with?