Word of caution….My recent purchase highlighted a change in fare rules whereby the stopover in London was allowed in either direction but with a charge of 200 Euro per passenger. The sting however was that the stopover could not be more than 10 days!!
Check the fare rules carefully they are hidden under two blue links after you have selected flights. The bottom one of the links for additional rules is in my experience the one that counts.
BA seems to be making a concerted effort to turn off the flow of UK passengers going to the EU to start the journey. But as others have said, the savings are generally such that the additional time involved still makes economic sense.
In my case the saving for 4 was in excess of £14,000 on the BA fare ex LHR even when the additional costs of going to and from Europe were added. It represented a 2/3rds saving! And this was not the cheapest option but I could not afford to night stop prior to starting my journey on this occasion!
No one can force you to check your bags to the final destination as per the ticket. Given their pitiful baggage handling, even in T5, a request to collect and check in again would be entirely reasonable.
I would add that whilst BA may wish to close off this revenue stream they need to understand that for passengers like me, Europe will remain my first choice of departure point. The research I have done on this suggests that most carriers provide the types of savings I have found from points in Europe and in some cases these are greater.