It depends. A number of classes of charities have a separate regulator so whilst they are legally charities, they are not required to register with the Charity Commission e.g. academies and free schools, further education colleges, universities and certain national museums and institutes. Other charities have historically been excluded from the need to register, but now these classes of charities are being gradually required to register e.g. individual church charities in longstanding denominations such as PCC’s in the Church of England.
Generally, if you are starting a new charity, unless you fall into one of the above categories, and/or your annual income is below the level of £5,000, you will need to register.