Our family of six is arriving at Heathrow on a day when the Tube is closed due to strikes. We originally intended to transport to our rental house in Hammersmith via the Piccadilly line, but that will no longer work. I have checked the 403 bus and it is either not offering service that day or is fully booked as it does not offer our date (8/6/15) as available. Does anyone have any suggestions? I saw a few shuttles but they appeared to only stop at hotels. Thank you.
Where did you get the 403 bus route from? The TFL 403 is in South London starting from Croydon. There isn't any direct TFL bus route - I would suggest a taxi but expect to pay a lot due to busy roads. Another possibility would be to ask the house owner - they may be able to arrange for a local minicab firm to pick you up at the airport.
There are deals for families and groups on the Heathrow express. For example, kids under 15 can go for free. Check here for the applicable discount deal and purchase you tickets online ahead of time.
https://www.heathrowexpress.com/tickets-deals/discounts-deals
Thank you all for your fast replies. Yes, the bus that I mentioned was National Express. It appears as though riding to Paddington then back out to Hammersmith might be the best route? That was also mentioned by the home rental company and some distant family friends who live near London. Our rental home is on Brook Green very near the Hammersmith Tube station. Unfortunately, we arrive early morning (around 7 am) so likely to be in the rush hours so we will likely need to camp out at the airport for a few hours until things quiet a bit.
Even if you don't go slowly if you are due to land at 7 in the morning, that is when lots of other planes land and you shouldn't count on walking through the frosted glass doors a lot before 9.
By that time most poor commuters will have completed pulling out their hair and be ensconced or nearly so in their London lairs, poor souls.
The super over crowded may now just be crowded, if you are lucky.
Heathrow Express and bus is what I'd try, at least for a while. Heathrow Express will likely work out but you will have to play the bus by ear.
Have you considered just using a car service?