Heather, Resources at Reigate Library were actually very poor for this particular quest, but had more luck at Redhill library as they had
some trade directories on microfiche.
First thing i looked for was the exact address so that i could trace the occupants, and that turned out to be 24 High Street. Using the the address and the trade directories I found the following :
In 1912, 1913 and 1914 - 24 High Street, AJ Miller Wholesale Tobacconist & Tea Merchants
1915 - 24 High Street, Webb & Rassell Wholesale Tobacconist & Tea Merchants
1916 - no info available
1917 - 24 High Street, Webb & Rassell Wholesale Tobacconist, Tea Merchants and Hair Dressers. They took out a Half page advert on p.152 of this directory
1918-22 no info available
1923 - 24 High Street, Arthur James Watson Tobacconist
1924 - 24 High Street Arthur James Watson Tobacconist at two locations
So we can deduce that Webb & Rassell took over an already established tobacconist and tea merchants in 1915, added a 'hair dressers' in 1916, and they themselves were taken over some time between 1918 and 1922.
The directories Redhill library don't have might be at the Surrey History Centre in Woking, if you wanted to narrow down any dates, but I think its fair to say that after the death of Mr Rassell in 1917 the business was probably taken over by Mr Watson fairly quickly. I did check in all the directories for any other business either Webb or Rassell might have had, but there was nothing listed.
Today 24 High Street is occupied by White Estate Agents, and the building is unchanged so you should be able to pinpoint it on old photos .. heres googles view of it
https://goo.gl/maps/CAEX4Hope this has been of some interest, and help !
All the best, and let me know if you want anything else looked up