If there is a dispuite over who is the current legitimate UK monarch can this be decided in court?

No, Parliament alone can decided who the Monarch is, they have decided that Queen Elizabeth II is the rightful monarch and therefore no court can overrule them. Plus the Act of settlement decrees that only the descendants of Sophia, Electress of Hanover are eligible to inherit the Throne. There is also no definite proof that Edward IV was illegitimate (DNA evidence is not available)