Do I have to include certain people in my Will? Can I disinherit anybody?

In general, the short answer is that you should include your spouse, children under the age of 18, and any dependants in your Will. Beyond that, you are generally free to leave anybody else out of your Will, but this doesn't mean that somebody else cannot make a claim on your estate, and it is possible that this claim could be successful. The most frequent grey area is with adult children.
If you die without a Will, your adult children are entitled to a share of everything that you own. Specifically, if you have a spouse and adult children, your spouse is entitled to the first £250,000 of your estate. Your spouse then receives half of everything else, with the other half being shared between your children; whether they be adults or young children.
However, there is no legal responsibility to include adult children in your Will. Your adult children may challenge the Will, but it will come down to a judge's decision as to whether that challenge would be successful. Most recently there was a case of a mother who disinherited her daughter and left everything to animal charities. A judge ruled that the daughter should receive a larger bequest, but the charities appealed and won their appeal. Even though the daughter was struggling financially, the Supreme court of England noted that "significant weight should be given to the wishes set down in a person's will and that family relationships do not automatically override the needs of charities"
Based on this ruling, it would seem that the law is consistent in only allowing a spouse, a minor child, and any other dependent to make a claim on an estate if they have been disinherited. There is no legal requirement to include an adult child, or former spouse or partner in your Will.