If you aren't interested in the route between FH and Bloomsbury, spare yourself from reading any further. It really is a niche interest.

OK, I can now announce the results.

IF everything is running fine, then marginally the quickest route is:
FH to London Bridge, Jubilee Line to Waterloo, Northern Line to Tottenham Court Road.

But almost as quick and with more frequent and reliable trains is the route via London Overground from FH to Canada Water, then Jubilee Line to Waterloo for the Northern Line. And as a previous poster suggested, unless you are in a perfect spot to sprint for the escalator down to the Jubilee Line at Canada Water, you may as well get on the front of the Overground train, go up to the main concourse at Canada Water and go down two escalators to the Jubilee platform. It's counterintuitive and may not actually save you any time but at least you feel like you are moving and you're not being funnelled into an unsafe space.

Coming back to FH, Southern Rail are so appallingly unreliable (except, bizarrely, on strike days) that it is far more reliable to come back via Canada Water to pick up the Overground train from there to FH. Even if you are in perfect time to pick up a connection at London Bridge, Southern have so many delays and cancellations that you will probably find you are standing around in the cold for 20 minutes or more wishing you had stayed on the Jubilee line to Canada Water.