"Fair comment. But looking at the various films and photos its clear something more than just an HV line is on fire"
The fire brigade have said that the fire is the result of a gas leak which has been ignited. They can't put the fire out until the gas is turned off because that risks an explosion if unignited gas is allowed to build up.
http://www.london-fire.gov.uk/LatestIncidentsContainer_01030482.asp#.VR0ZeOFIlfA
The loss of Internet will be down to the cutting off of power - not all telcos back up everything with generators - and in the case of companies like Verizon and Colt it'll be because their privately owned fibres are routed through the same tunnels - there's a lot of telco cabling running through the Kingsway tram subway.
Citadel / Kingsway was built to be impervious to external events - bombs, fires, military action - it seems pretty unlikely that an unrelated fire nearby is somehow going to leap through earth and mud and then through a cast iron tunnel wall into a different set of tunnels.
If Citadel was on fire, Chancery Lane tube station would be closed. It's not, trains are running normally.