This is not the case. As you just read in the article:

https://highwaycode.org.uk/rule-140/

> Cycle lanes. These are shown by road markings and signs. You MUST NOT drive or park in a cycle lane marked by a solid white line during its times of operation. Do not drive or park in a cycle lane marked by a broken white line unless it is unavoidable. You MUST NOT park in any cycle lane whilst waiting restrictions apply. Law: Road Traffic Regulation Act 1984: Sections 5 & 8

Here's a cycle lane with a broken white line: https://www.google.com/maps/@51.5159626,-0.1020373,3a,75y,17...

You shouldn't enter, stop or park here unless it is "unavoidable". You're a taxi driver dropping off a passenger? That's not "unavoidable".

Here's a cycle lane with an unbroken line: https://www.google.com/maps/@51.5162184,-0.1047894,3a,75y,15...

The latter, no you CAN'T enter it to drop people off, no matter who you are. It is literally illegal to do so.