If a married couple both die then the courts will appoint the legal guardian(s) for your child(ren). When you make a will you can specify who you wish to be the legal guardians so that your wishes are known but it won't automatically happen. In my case my SIL and BIL are named as legal guardians but if DH and I were to both die, the courts would verify that SIL and BIL were suitable. If, for example, one of them was incapacitated in some way, some other member(s) of the family could be appointed instead.
If you aren't married then it may be even more important to have a will since the inheritance situation is more complex. You wouldn't want your child to end up in care for a few months while your legal affairs were being wound up.
It takes about an hour for a solicitor to draw up mirror wills for you and your partner, and costs about £135. It is definitely worth getting it done by a solicitor as they will tailor it to your specific circumstances. Also there are complications such as if one partner dies within a month of the other but not at the same time, e.g. if you were in a car crash and one died immediately and the other several days later. I know it's not nice to contemplate such things but if that happened without a will, your estate would be tied up for a lot longer than if both died at the same time. So there would be no access to funds for any expenses incurred by your children, or for any funeral costs.
If the cost is prohibitive then a DIY will kit is better than nothing since at least then your wishes are known.