Most of our connections are via LHR. While the true low costs carriers do not seem to operate from there as frequently, we have always found the connections on BA to be well priced and frequent. In fact, we have avoided the low cost carriers because their flight times have never worked with our connections, not to mention the lack of AA miles. Have also done LHR-CDG easily and cheaply when ORD-CDG was priced too high, although this opens up the whole debate on flying v. Eurostar.
That said, if you can avoid the zoo at LHR, do so. We had great connections through BRU and DUB last year.