The airfare for a round trip from the US to England is much cheaper
than the fare for the same 2 flights taken in the opposite direction.

For example, on Virgin Atlantic the fare is $762 if the round trip
leaves from London, but only $474 if the round trip leaves from Newark
(LON-EWR, 3 weeks advance purchase, midweek flight, returning middle
of the following week).  So taking the same 2 flights from London
costs 60% more than it does from the U.S.!

My question is - how can someone who wants to take a round trip from
London get the better price?

I expect that if someone needed to take 2 round trips, they could book
one round trip from London and one from the U.S. -- make the 1st and
4th flight a round trip from London and the 2nd and 3rd a round trip
from the U.S.  That gives one of the trips at the lower fare.  (It
might be best to do this on 2 different airlines, sure.)

How can one do better than this?  Thanks!

How about booking a round-trip  **with open tickets** from US . that
will give you 2 coupons, open ended (no specific date) - 1st for
EWR-LON flight and 2nd for LON-EWR flight. Then you board a flight at
LON showing/using the 2nd coupon, and later use the 1st coupon for
EWR-LON. If you book yourself an E-ticket, chances are that this will
definitely work. But then I am not sure about it. Let me know if it
works.

As someone who has flown regularly on round trips from England to the
US over the last five years, I would heartily recommend booking such
tickets through a third party discounter rather than the airline.

I use Dial-a-Flight frequently and have also used other companies, all
of whom are notably cheaper than the airlines themselves even for the
same flights.