Remarriage - Legitimate Ground For Relocation: I have custody in Israel and am divorced from my child's Israeli father. I have been dating someone with a business back in the UK. If we got married, would I be allowed to move to the UK with my child even if his father disagreed?

There is no guarantee of this, but remarriage is considered a legitimate ground for relocation. If you filed for relocation in Israel based on remarriage to someone with a livelihood abroad, who could not easily live in Israel, you would have a reasonable chance of success, assuming that the professional reports recommended that this was in your child's interest, given all the circumstances and options.
Relocation From Israel