This old chestnut
It is just Bernie bluster and aimed at the BRDC and Silverstone. There is a break clause in the FOM contract with Silverstone that allows both sides to walk away from the deal after 10 years of the 17 year deal. While the break clause doesn't come into force until 2019 both sides need to give a commitment to continue or decide to activate the break clause a number of years in advance, so they have plenty of time to make alternative arrangements.
Silverstone has a cheep deal at around 23 million for the hosting fee, while most other tracks pay in excess of 40 million some as much as 70 million. As has been mentioned before on this thread, Silverstone is up for sale to the Land-rover/Jaguar group and I'm sure FOM want assurances that this deal will not cause the BRDC to pull out of the current contact after 10 years.
Also the teams all want a British GP as it is considered a home race for many of them and there isn't really another circuit available at the moment without a lot of investment to improve facilities and that is willing to pay the hosting fee.
Holding a race in London wouldn't be easy, there would be loads of objections from people living near the circuit and who would pay for it? While there has been a change in the law allow local authorities to close roads in order to host motor races, in central London rich people would not want the disruption and kick up a massive fuss, even legal actions which could take years to sort-out. The government has made it very clear many times that it is not prepared to put any money into F1, may be the new Mayor would chip-in if there was loads of private money also being pledged, but I think that unlikely.
Were they to chose somewhere like Hyde Park and stay off public roads then maybe it would have a chance, but again there is the big question of who would pay the cost, with hosting fees and other expenses, it is likely to cost anything from 50 to 80 million. Also what would be the gain for London? It is already the top city destination for tourist with over 17.5 million a year and apparently Hotel occupancy rates are at an all time high, I don't see the benefit.
I'd love to see a street race around London I just don't think it will happen.