Under English law, nobody is ever obliged to leave a single penny from their estate to any of their relatives. (There are five beneficiaries of my will and not one of them is related to me). Anyone is free to leave their estate to whoever they want to.
In general, the courts will always (rightly) uphold that principle. However, upon the death of a testator, certain people (including the children of the testator) have the right to apply to a court for an order varying the terms of the testator's will on the grounds that the will failed to make 'reasonable financial provision' for them. It would then be up to the court to decide whether the provisions of the will should be varied.
However it should be made clear that simply saying "I was the testator's son/daughter, so therefore I ought to get something from their estate" is most definitely NOT a valid reason for having the terms of a will altered. Many people are determined that their offspring won't get a single penny from their estate and, as previously stated, the courts will generally respect their right to come to such a decision.
A court would be more likely to vary the provisions of a will where the claimant was, immediately prior to the testator's death, being maintained by them. So, for example, a disabled child of the testator, who was living with the testator and being supported by them up until the time of the testator's death (but who was omitted from their will) might well be able to get the will changed so that they continue to be supported from the testator's estate.
Similarly, if a student was part-way through a university course when their parent (who had been helping them fund their studies) died and then found that he/she had been omitted from their will, he/she might well be able to convince a court that they should continue to get funding from the estate.
As indicated above, it is entirely a matter for the court to decide as to what amounts to 'reasonable financial provision'. However a basic framework for the court's decision making is laid out within the relevant legislation (see Section 3), which you can read here:
http://www.legislation.gov.uk/ukpga/1975/63