Q: What is the cheapest transportation option for four (4) people going from Gatwick Airport in the UK to London (Citadines Apart’Hotel Holborn-Covent Garden? How much would a taxi cost?
A: In my view, the cheapest way to get from Gatwick airport to Covent Garden is to get the Gatwick Express train into Victoria and then jump on the underground to Covent Garden station (you will need to change once, at Green Park). I think the Gatwick Express is £13 per person, and the underground ticket will probably be around £2 each.
The cost of a taxi would depend on the time of day you travel. But unless you book it in advance to meet you, a metered black cab from Gatwick to central London would probably cost around £80 or even more. (And may not be able to carry more than 3 people with luggage, anyway)