(Just trying this again, as I was using my referral code the first time)
MyTaxi have released an app for London. It's similar to Uber but it's for black cabs instead.
You can get £10 off using the promo code london.ten
Also, they're offering 50% off off-peak fares until the 28th of May, which seems like a good deal.
Android link: -https://play.google.com/store/apps/details?id=taxi.android.client&hl=en_GB
Apple link: -https://itunes.apple.com/gb/app/mytaxi-the-taxi-app/id357852748
50% discount applies to the metered taxi fare on journeys that start and end within London. 50% applies to in-app card payment only at point of payment during off-peak hours. Off-peak is Mon - Fri 0900 - 1700 & 2000 - 0700 + anytime all weekend. Tip to driver not included in discount. Offer ends at 23:59 on Sunday 28th May. For full details visit uk.mytaxi.com/fifty