At least in theory only Congress can declare war. In theory the UK Prime Minister can do so on his own. We believe in separating the judiciary from the legislature in theory, but the Head of the judiciary is the Lord Chancellor, who appoints all the other judges, and he in turn is appointed by the Prime Minister, sits in the House of Lords, and is a member of Cabinet.
This last point is what the dispute in UK is all about. The Labour Govt. quite rightly imo, wants to separate the Lord Chancellors office from the legislature by kicking him out of the H of L and forming a separate Supreme Court. Meanwhile as we adopt a more republican flavour to our constitution, the US appears to be going in the opposite direction by having Presidents chosen from an ever decreasing number of mega rich families. Eventually it will be only one, and hereditary monarchy will be established.
There have been a number of "lineages" in the US presidency. The Adams's are the best known but there were also the Harrisons, Roosevelts and now Bush. This tends to go in cycles,