If the tube strike is going to leave you stranded on Wednesday and Thursday, you may want to give one of the app based cab services a go.
These codes are all HfP ‘refer a friend’ codes except for Hailo:
Uber – £15 off your first ride with code headforpoints – download here
Hailo – £10 off your first ride with code STANDARD10 (expired 31 Aug)
Gett (ex GetTaxi) – £10 off your first ride with code GTSZFWS – download here
Kabbee (pre booked minicabs) – £5 off your first ride when spending £10.01 or more with code [deleted as now expired] – download here
Uber will presumably be running surge pricing for much of the day. This means that you will pay a multiple of the standard rate. The rate generally increases to match supply and demand which means, if you are prepared to pay the price, you have a fair chance of being able to find a car.
That said, Uber was strangely quiet during the last tube strike – I had no problems getting a car at the standard price in Chelsea and South Kensington on two occasions, albeit both outside rush hour.