Just to add on this point of transit, this is taken from Timatic which is what check in agents for your flight to the UK will see and will be checking you against. This seems deliberate, not merely an oversight of not exempting transit.
3. Effective 7 December 2021, 4:00 GMT, passengers entering or transiting through the United Kingdom must have a negative COVID-19 antigen, NAAT, PCR, LAMP or LFD test, taken at most 2 days before departure from the first embarkation point.