Webb Richardson's first football experience came with Barnet Alston, forerunners of the current Barnet club.

He signed for Leeds City in June 1913 and was tried in pre-season games, when the Leeds Mercury remarked that 'he is a clever player, has a fine turn of speed and shoots well.' He had to be content with reserve team football that season, though he came close to a debut in December with the regular choices not living up to expectations.

Richardson made his first senior appearance on 19 September 1914, at home to Blackpool, the fourth different player to fill the role in five games. Reports claim he acquitted himself well in a 2-0 victory, though he 'could have improved upon his corner kicks'.

Richardson played again the following week, in a defeat at Clapton Orient, when 'the City forwards were very weak, and rarely did they hang well,' according to Metro in the Leeds Mercury. He never appeared for City again and left Elland Road at the end of the season.