Not that strange considering the government is more interested in protecting the City of London than London City. Look at the the money the government spent and the re-engineering they did post Bishopsgate bombing to prevent the financial centre being a target again to the Provisional IRA. They completely redesigned the layout to decrease the number of ways in, roads where blocked off with bollards, or they built houses / office buildings to block off routes. The whole network is monitored by CCTV and you can follow a car entering one side of London, through it and out the otherside from one control room.
Belfast had the first "Ring of Steel" to prevent terrorists bombing the city centre. But the City of London couldn't have such an ugly looking example. So they got creative and a whole industry sprang up around "anti terrorist architecture".
Sorry to be anal but there isn't "London City" there is only the City of London of the tow you mentioned. Greater London is an English Region and though essentially a big metropolitan area it is not officially a city itself, it does contain two areas that have city status...
The City itself is a unique relative to other local authorities in various ways and there are relatively few residents but a whole load of employees/companies... ergo they're stinking rich as far as local authorities go.
So your point re: their nicely dressed up anti-terrorist infrastructure might have nothing to do with "the government" favouring the city with regards to spending money, they've got plenty of money themselves to spend on infrastructure and they have their own police force (separate to the Met) two police the approx 2 square miles of the "square mile".
Incidentally it was apparently City of London firearms officers that dealt with the terrorist in this incident.