The Senior Regiment of the British Army

There is some possibility for confusion here. The oldest regiment in the British Army is the Coldstream Guards, which was first recruited by General George Monck in 1650 as part of Cromwell's New Model Army. The Life Guards Regiment grew from the four troops of Horse Guards raised by Charles II in 1660, but is regarded as the senior regiment because it's always been a part of the regular army, while the Coldstream Guards has not.

The wording of the question is further justified by the reference to the Household Cavalry, which indicates the Life Guards as opposed to the Coldstream Guards.

Wikipedia makes no bones about it: the Life Guards, it says, "is the senior regiment of the British Army", while the Coldstream Guards "is the oldest regiment in the British Army in continuous active service".