Until about 25 years ago, Welsh and Jeffries was owned by Sidney Boddy, the owner of John Walls, also of Eton. The Saville Row operation of Welsh and Jeffries, had been a separate business, under different ownership, for many years even then. Mr Boddy retired, and the Eton business was sold.
W&J Eton were my own tailor from about 1964 until the late 70's. I have not been there since, but recently were in touch with them again. I was very surprised at the low prices quoted for true, hand made, bespoke. They claim to have their own workshops, but the prices quoted were almost certainly for factory made.
The key to good bespoke is the person who measures and cuts the suit, and the coat and trouser hands who make it up. When ownership or staff change, there will always be a change in the nature of the product they make. This will inevitably result in an improvement or deterioration in quality and fit. So the name of the establishment is less important than the key people involved.