If arriving at LHR on BA, then a connecting flight on BA is relatively easy. If arriving on another carrier, it is sometimes easier to get into central London than it is to schlep to a different terminal at LHR.

I have literally made this transfer 40 or 50 times. Virgin Trains is usually the easiest/cheapest option, especially if you purchase your ticket in advance. However, if your trip happens to coincide with Network Rail planned engineering works, flying might be the preferred option. (One of my transfers coincided with planned engineering works and the best routing I could find at www.nationalrail.co.uk took nearly 6 hours and required 3 connections.)

For reference, advance purchase tickets on Virgin Trains are often £11 each way. (Train tickets are available for purchase 90 days out). Advance purchase tickets on BA are often as inexpensive as $50 each way. However, as others have noted, the fares for both climb steeply closer to departure.