Once you have the route down you'll increase in confidence and you'll grow a sixth sense for traffic and any turmoil that might occur. Then after a few weeks doing the same route and getting used to london routes you'll find your self using your bike more and more as you'll be used to london cycling. Then the city is yours!

The side-streets are frequently fine as long as you carrying out caution (i.e. riding a door's width from parked cars.) The main roads are noticeably more intimidating, however the roads themselves aren't the real issue (although if you're a unsteady cyclist I would steer well clear.) Most injuries go down at junctions.

Never pass on the inside of a vehicle turning left. Never pass on the inside of a bus, truck (lorry) or van. Watch out for taxis: they repeatedly stop to pick up fares at the side of the road. Be a good road user: pause at the traffic lights, even if others don't! Also, pedestrians, predominantly in touristy parts (like the Strand!) often saunter out into the middle of the road with no looking, unmindful toward their surroundings.

If this all sounds a bit intimidating: elsewhere in the thread it looks like you are near as makes no difference to the Finchley Road. The number 13 bus runs straight to Aldwych, so you can get it directly to KCL. (Aldwych is a curved street on the end of the Strand, forming a sort of lowercase b shape—KCL is on the Strand, right amid the two junctions with Aldwych, next to a building called Somerset House.) You could also, should something happen (e.g. traffic problems on the Finchley Road), walk to Hampstead Heath and pick up the number 24 to Trafalgar Square, and then walk down the Strand to KCL.