I can't speak to the U.K., but in the U.S., the answer is: it depends. Typically, a search warrant will be limited in scope, whereas a consent search will not

I can't speak to the U.K., but in the U.S., the answer is: it depends. Typically, a search warrant will be limited in scope, whereas a consent search will not be. In fact, law enforcement is usually trained to ask for consent to search even if they have a warrant, because it precludes a lot of legal issues. For example, if they are executing a search and they see something out in the open that suggests some other crime but isn't conclusive, and they want to search for more evidence related to that other issue, they are supposed to seek another warrant unless an exception applies (e.g., exigent circumstances). If they have consent to search the house (or car, or ...), then they do not need to stop, and they do not need to worry about the evidence being excluded if the judge disagrees that there were exigent circumstances. For this reason, I think a lot of the reactions in this thread against compelled evidence are misplaced. A victim is much more likely to implicate herself or himself in collateral conduct in a consent search than they would be if the evidence were compelled. A search warrant, for example, would likely be limited to text messages between the alleged victim and the alleged perpetrator... and not include, e.g., text messages between the alleged victim and her/his drug dealer. Defense access will depend on discovery rules, which vary widely between jurisdictions. Either way, it won't be admissible in court unless a judge rules that it is relevant to the case.