4 hour layover at Heathrow - do I have time to see Westminsterb by train or cab?

No. Not only is there travel time to and from London, you'll also have to go through airport security again.

No. On a couple of occasions, 4 hours was barely enough time to change terminals. Heathrow is mayhem defined.

No - you will be lucky to get through passport control and security in that time, depending on number of large planes that have landed around the same time as your plane.

There's not enough time, but let's not over-exaggerate Heathrow.

A couple of weeks ago I was waiting for the shuttle to the car places twenty minutes after I stepped off the jetway -- this in the morning crush. I'm unrushed if I crack the terminal door outbound at an hour and a half prior to departure.

You posted this question in the Trip Reports section of the Forums - where trip reports are posted, not questions.

Questions are put in the appropriate question area, in this case England because according to Rick Steves sense of geography there is no UK, where they will be seen by people prepared to answer them.

In the meantime, I will say you have no chance.

An hour for arrival formalities, 3 hour minimum for international flight check in formalities, there's your 4 hours.

An hour for arrival formalities, 2 hours (if you are brave) minimum for domestic flight check in formalities and you have one hour to kill. An hour into London, and hour back and no time for seeing anything and oops you missed your flight by an hour.

You definitely will not have time. Now, I will tell you that getting thru immigration and such was extremely fast that last three times I traveled to Heathrow (I'm from the USA), you still will have about 2+ hours to play. But, since you are located outside of London, regardless of how you choose to travel, there will not be enough time to do anything within London city limits. My suggestion is to go to one of the lounges within Heathrow - some areas have massage therapists available, plus there are a million places to shop - and relax for a bit before continuing your journey.

Good luck,
Lisa