Is there a hotel shuttle bus from Paddington Station to nearby hotels?

Our family of 4 will be traveling to paddington station from the airport and will have several pieces of luggage. We are staying nearby at the Royal Lancaster. We understand it is normally walking distance but with the family and cases are wondering if there is a pay for shuttle or should we try a black taxi(we... show more Our family of 4 will be traveling to paddington station from the airport and will have several pieces of luggage. We are staying nearby at the Royal Lancaster. We understand it is normally walking distance but with the family and cases are wondering if there is a pay for shuttle or should we try a black taxi(we just didnt know if the taxi would overcharge us for so short a ride). I heard there was something called the "hotel express" but could not find a website that describes such a shuttle. Thanks!
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