I shouldn't worry about the tube strike too much. It is only one union (the RMT) going on strike, their impact will be very limited.
HOWEVER, there is a more serious problem for people travelling across central London. For the next 6 weeks The Mall will be completely closed for resurfacing (we can't have Her Majesty's drive being uneven can we), this should cause the worst congestion in London for years.
Those taxi journeys could prove long and expensive for the next 6 weeks.
MF