I think Pearsons used to be on The Upper Richmond Road in Sheen.
I think they ( or perhaps a later name) closed 5 - 10 years ago, maybe more.
Action Bikes is on the other side of the road.
there’s a shop called Bicycle further up in the direction of Richmond
https://www.bicyclerichmond.co.uk/
Edit
Pearsons are still in Sheen.
https://www.pearson1860.com/our-sheen-store/
But not the shop I was thinking of, that was a small corner shop nearer to Richmond. It may now be Savills.