The large night-time events over the weekend will have a taxi company working with the venue to provide taxis should you need one. This may cost more than booking in advance and you may have to queue.
To avoid waiting you may like to book a cab in advance from one of the most reputable taxi companies in London, Addison Lee
Addison Lee Online Booking
Addison Lee Phoneline – 0844 800 66 77
Or sign up to Uber – https://www.uber.com/ and get a cab on demand
Local Taxi companies are easily searchable online in addition to Addison Lee and Uber cabs.
PLEASE NOTE: Tower Bridge will be closed from 1st October – 30th December. The closure will be in place 24 hours a day, 7 days a week. Please read the Transport for London website for more details: https://tfl.gov.uk/status-updates/major-works-and-events/tower-bridge-closure