To try to summarise the important bits of what's above (and to add a few more important bits):
1. If you own your home with your partner as 'joint tenants' then the laws relating to both wills and intestacy are TOTALLY IRRELEVANT anyway. If one of you dies, the other will AUTOMATICALLY become the owner of the property. (Nothing written in a will can change that).
2. If you and your partner own your home as 'tenants in common' then each of you is entitled to leave your share of the house (which would normally be a half, unless otherwise agreed) to whomever you choose in your wills.
3. Similarly, if your partner owns the whole of the house he can leave it to whomever he chooses in his will.
4. When someone marries their will is AUTOMATICALLY rendered invalid UNLESS it was written 'in contemplation of marriage'. (That phrase must be included within the wording of the will. Further, the testator must have genuinely been contemplating marriage at the time that he/she wrote the will).
5. When there is no valid will (which, of course, includes the circumstances where a will has been invalidated through marriage) the laws relating to intestacy apply. They are explained in the flowchart here:
http://www.manchesters.co.uk/Intestacy-flowchart.php
or you can work through this:
https://www.gov.uk/inherits-someone-dies-without-will
6. As you'll see from the above links, the partner of a deceased person has, in the first instance, NO RIGHTS WHATSOEVER to inherit anything from them (unless they were actually married to the deceased person or in a civil partnership with them).
7. Under the provisions of the Inheritance (Provision for Family and Dependants) Act 1975, a person who has lived at the same address as a deceased person, as if they were their spouse, has the right to apply to a court to VARY the terms of their will (OR to vary the intestacy rules) in order to receive 'reasonable financial provision'. So, despite what I've written above, an unmarried partner of a deceased person MIGHT actually be able to receive an inheritance from their deceased partner. However the court procedure is COMPLEX and EXPENSIVE, so it's FAR better to get things properly sorted out before the death occurs.
8. I've deliberately avoided using the term 'next of kin' above, as it has no single meaning. As far as this question is concerned, my links in paragraph 5 above (explaining the intestacy rules) are what matter here. Elsewhere (as in nominating 'next of kin' when you go into hospital) you're free to choose anyone you like, irrespective of whether you share any relationship with them.