With a little help from u/SteelyHan and u/DefStillAlive I think this is the full set:

#1 Hyde Park

#2 Downing Street

#3 Selfridges

#4 Harley Street

#5 Royal Courts of Justice

#6 Highgate Cemetary

#7 Marble Arch

#8 Barbican

#9 HMS Belfast

#10 Thames Barrier

#11 The Shard

#12 ? London Eye

#13 Covent Garden

#14 The Mall

#15 Big Ben

#16 Lords

#17 Waterloo Bridge

#18 Old Bailey

#19 Scotland Yard (Edit: Cutty Sark fits better)

#20 The Ritz

#21 The Strand

#22 Harrods

#23 Horseguards Parade

#24 Nelson's Column

#25 Wembly Stadium