I contacted the London Cabbie and YouTuber:
Tom the Taxi Driver Here he confirms the costs:
1. Only Green Badge taxis that have completed The Knowledge of London are allowed to apply for a “tag”. It’s a card that can have credits applied to it and sits within a cradle called a booster.
2. From memory, the booster was approximately £15-£20, as was the tag card. 1 credit to enter the feeder park costs £7.20. You have to purchase a minimum 3 credits at a time.
3. It all depends on time of day and circumstances. In recent post Covid times due to a shortage of drivers, currently it can run around 2-3 hours as an average, but at night it can be as quick at 20 minutes. This however is risky, as you run the chance of all the flights landing and no more passengers coming out, meaning you have to wait on the rank until the early morning once flights resume to get a job (or you can leave the rank and forfeit the £7.20 you paid).
So they have to pay for the card and booster (which registers the card to an automatic reader and that was about £30/40 one off) then £7.20 per fare but having to buy 3 at a time means that LHR gets their money upfront some days before it used. They have to go into the Feeder Park and then (in sequence) wait until called and told which Terminal to go to. They may have to wait 3 hours (or more) to get a fare.
When they drop a fare at a Terminal, they are not allowed to immediately pick up another but must go to the Feeder Park - or leave LHR.