Whilst there is no legal requirement for you to make a will it is highly recommended once you have purchased a property, whether you are single buying on your own or with a partner or spouse.
In the situation of an unmarried couple - despite having bought a home together, if you are not married or in a civil partnership, (whereby, in both cases, your rights of inheritance would be automatically guaranteed), it is strongly advisable to get wills made ASAP.
Ultimately, everything hinges on the basis of the technicalities of who actually bought the home. For example, many people talk about "buying a home together", when in fact only one of their names is on the deeds - so from a legal standpoint they are simply co-habiting.
On the other hand, while you may indeed have bought your home in both names, there are actually two different ways in which property can be jointly owned, with significant legal differences between them. So, if you own the property as "Joint Tenants" you are basically both equal legal owners, with each of you automatically becoming the sole owner in the event of the other's death - will or no will. However, if you own the property as "Tenants in Common", then the surviving partner has no automatic right of inheritance, and the dead person's share simply becomes part of his or her estate, to be distributed either according to the terms of any will they may have, or according to the rules of intestacy (which in practice means that it goes to any living relatives in a strictly laid-down order of precedence, or even reverts to the Crown). In such cases, the only recourse open to the surviving co-owner would be to buy out the deceased's share.
So, the first thing you need to do is to clarify precisely on what basis the property is owned. If only one of your names is actually on the deeds, then it is absolutely imperative that that person makes a will, otherwise the surviving partner has no rights of ownership or inheritance whatsoever. Similarly, if you own the property jointly as Tenants in Common, then both of you should make so-called "mirror wills", whereby each of you become both sole beneficiary and sole executor to the other. If on the other hand, you own the property as Joint Tenants, then you will both automatically inherit. Regardless, it is still highly recommendable that you make wills anyway, just so that everything is covered and essentially for peace of mind.
In the meantime, take care and good health!