@screenman lived in Twickenham in the past
Pearson’s are quite recent to Sheen (unless they were there years ago too). They’ve been in Sutton for ever (founded 150 years ago but don’t know where original site was).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.