Yes, you can fundraise if you are not a charity. However, if you are not a charity you cannot raise funds as a charity. This is an important distinction because there are some benefits to being a charity that are not afforded to an individual fundraiser. These include things like being able to claim charitable status and not being able to offer tax relief on donations.
If you intend to raise money for a charity, then consider getting them on board with your fundraising before you start. They may be in a position to offer you additional resources, support, promotional materials and other forms of assistance.