Mogg's Table of the new Watermen's Fares, published in 1828 cites a rate of one shilling¹ per half hour for 6 customers (i) suggesting the waterman in the song is asking an exorbitant rate.

Reference:
(i) Regency Reader website www.regrom.com/2017/03/08/regency-travel-wherries-on-the-thames