I used to write wills for a living and I've never encountered a 'cohabitation agreement'.
Barry's draft above looks fine to me. The only addition I might make to it (although it's far from essential) is the following wording between sections 1 and 2:
"I hereby revoke all former Wills and testamentary dispositions made by me".
(It's common practice to include such a term, even when no previous will has been made, to save the executors having to look for an earlier will which might still have valid provisions within it).
Your partner can be one of the executors of your will (or the sole executor of it) but must NOT be one of the witnesses to it. The witnesses must actually SEE you sign your will. (i.e. your will won't be valid if, for example, you sign your will at home and then take it to a witness's house for them to sign it). It's also best if they actually see each other sign too. (I'd add the following wording before the witnesses' signatures but, again it's not essential "Signed by the said [your name], the Testator, as and for his Last Will and Testament in the presence of us both at the same time who, at his request and in his presence and in the presence of each other, have hereunto subscribed our names as witnesses").