As far as I know there are certain criteria for forced entry to a private home but.....this would be for a high level offence such as but not limited to imminent reason to stop an act of terrorism or atrocity, threatening the life of the Monarch and or heirs, serious domestic violence, abuse of the vulnerable etc.
Most visits by plod other than doorstep waffle relate to informing relatives of a death/accident/injury, returning a wayward youth and asking "does this belong to you" firearms offocer inspecting security etc
Blair muddied the waters years back by making traffic wardens enforcement officers, David Icke reports they have special undefined powers including entering a property should police be involved in bigger nastiness going on at some undisclosed future date.
Common law and European law were both practiced here as was/is Imperial weights and measurements alongside metric.
European law is a alien to common law is so much as common law says everything is allowed unless expressly forbidden (not for biden though).
So the short answer is I am not entirely clear about forced entry and aggression if allowed entry by resident without showing a warrant as courts tend to side with the plod. All appearances of plod with a warrant by it's nature allow entry to detain suspect or search premises.7
Scotland retained many of it's own laws after 1707 and is different in some examples than common law and what they would be I have no idea