Blackberry Cars Airport Transport

No, I've never heard of them. Sounds like a minicab firm. It will all depend on who's driving that day, how long he (or possibly she) has been driving a car in England and how long in London, but at the end of the day if the tubes are on strike unless they give their drivers a flying carpet they won't get there any faster than a professional driver.

If you want a taxi that knows all the routes and all the rat runs and make the best of a bad thing use a black cab (no the colour is not always black - it is a shorthand term for a licensed hackney carriage in London) and be prepared to pay for the slow traffic as the meter keeps ticking.

Or use Just Airports. I don't have a personal experience with them, but they get very good reviews on this Forum, including just today if you read Susan's Trip Report (from Susan and Monte) who just got back and had 2 very good experiences with them.

If you don't have a lot of luggage, the suggestion made by Marco in the tube strike thread is an excellent one which is likely to be least impacted by the strike (and cheap too) but you must be traveling reasonably light:

An alternative would be 285 bus from Heathrow to Feltham, train to
Clapham Junction, then Overground to Whitechapel. This is the start of
the Overground route. Under 'normal' conditions the journey time for
this would be roughly the same as the Express/bus journey, but may be
better in congested roads - and would be cheaper. The Overground
though is busy all day whatever.

Thanks for putting in your 2p, Nigel. I just read Susan and Monte's trip report and saw their recommendation. We're still considering Marco's suggestion unless a carry-on each will be too much luggage. I will echo the sentiment from the other "strike" postings that we would feel left in the lurch if you drop out on us! In the meantime, I'm sending a lot of positive vibes for strike resolution.

My husband and I have used "Blacklane.com". They are a very reputable company based in Germany. We just used them to go/from to LAX (Los Angeles), Singapore, Japan and Hong Kong. Our transfers were in Mercedes automobiles. The drivers met us at home, at our hotels or as we picked up our luggage at the airports. We would totally use them again when we go to England or wherever we go.

Car Services, courtesy of TA:
http://www.tripadvisor.co.uk/ShowTopic-g186338-i17-k4886933-POLL_Airport_Car_Service-London_England.html

Thank you for adding more info, Elaine and Harley!