Vintage Monopoly Game: What Year is it?
If the box looks like the images below, I'd say it's from the 1950's which is when all the mentions of a board with that trademark number appear to be dated.  I've found examples estimated at 1955 and 1957 for year of production (linked below).



http://www.cathyscollectables.co.uk/pages/Vintage_Game_Waddingtons_Monopoly_Board_Only_P_711981_Circa_1957_England_258870-z=879773&amp;p=108919.cfm

https://www.oxfam.org.uk/shop/toys-and-games/games/john-waddinton-vintage-1955-edition-monopoly-trade-mark-711981-hd_101549207