If you have been working with King's College London and then moved over to King's Teachers part way through the tax year (6th April to 5th April of the following year), the P45 you receive from King's Teachers will contain the previous earnings and deductions from the engagement you had with King's College London directly, this will appear under "Previous Employment". The remainder of the P45 will detail the earnings and deductions with King's Teachers.
If you are to review this on the HMRC portal, both employments may appear to be either combined or separated.
For any further assistance on this topic please contact the King's Teachers Help Team kingsteachers@kcl.ac.uk