BS 7671 is the UK requirements for electrical installations standard, also known as the Wiring Regulations. Appendix 4 (BS 7671:2018) gives guidance determining the current capacity and voltage drop for cables.
Cable current capacity calculations in BS 761 are based on the derating factor method, see Cable Derating (Factors). The derating tables have been derived from IEC 60287 and aligned with IEC 60364 (although there is some fundamental difference).
The parameters considered in the standard are, ambient temperature, soil thermal resistivity, the installation methods and grouping of cables.