Possible Clues:

• Tree that becomes an adjective when "u" is inserted
• East London area, much favoured but not upper-class
• Central character is removed from well-liked tree
• Tree is liked by all, though non-U
• Tree; east London area
• Aspen
• Tree — part of London's Tower Hamlets
• Part of London appealing to the general public but not suiting the toffs?
• Tree with light, soft wood and catkins
• Wood's in demand, we're told yew's dis­counted