No, quite simply, C_t is applied to It, before It is put into the other formulas, and only applies where the design current is significantly less than the effective current-carrying-capacity chosen. This is explained in Section 5.6 of the IET Electrical Installation Design Guide.

I take it you mean Ci is applied to It before being put in the formula for calculating Ct? In any event, to operate the formula in 6.1 of Appendix 4 of 7671 one must establish the value of It by using either one of the conventional two methods. To do that all correction factors including Ci, Cg, Ca etc are employed. That being the case, why is Cg, Ca etc used to calculate Ct and Ci is not? 

From Design Guide;

Say in the example above, Cg was 0.78 and no other correction factors applied, Ct would approximate to 0.99, and not worth employing. On the other hand, if Ci was 0.78 and no other correction factors applied, the outcome is 0.94, the same as for the example given above. 

I take it you mean Ci is applied to It before being put in the formula for calculating Ct? In any event, to operate the formula in 6.1 of Appendix 4 of 7671 one must establish the value of It by using either one of the conventional two methods. To do that all correction factors including Ci, Cg, Ca etc are employed. That being the case, why is Cg, Ca etc used to calculate Ct and Ci is not? 

From Design Guide;

Say in the example above, Cg was 0.78 and no other correction factors applied, Ct would approximate to 0.99, and not worth employing. On the other hand, if Ci was 0.78 and no other correction factors applied, the outcome is 0.94, the same as for the example given above. 

why is Cg, Ca etc used to calculate Ct and Ci is not? 

I’ve never really given that any thought. I just follow the design sequence starting with determining the final circuit overcurrent protection devices and cables, incorporating the thermal insulation factor (Ci). Once the tabulated current-carrying capacity of the cable (It) is identified in Appendix 4 of BS 7671, the next step is to perform voltage drop calculations. The design guide I use, the calculations for the correction factor (Ct) consider only the ambient temperature and grouping factors. Same as the Ct formula you have shown but without Cs and Cd factors.