Yes, the supreme court that we have today in the US is a really good thing that does a whole lot of good for our country, and makes all of the laws that we have today be held up in a way that is fair to the people by the constitution.
Yes, I believe that Britain could greatly benefit from having a equivalent of the Supreme Court. The Supreme Court is a valuable part of the judicial system. It sets a precedent for laws that may not have been visited before for all the lower courts to follow. The Supreme Court is a useful tool for people to be able to take their lawsuits to another level of court if they find the lower court's decision unsatisfactory.
While there is The Supreme Court of the United Kingdom with many similarities to the United States version, it is limited in the types of cases it can hear and laws it can overturn. I believe that such limitations have led to political corruption in the United Kingdom and such restrictions should be lifted. This would make the law more relevant to, and protective of, the British people.
I think historically this could have been a useful thing for the United Kingdom, but since the advent of the European Union, and the various bodies overseeing law such as the Court of Human Rights, and various other bodies that provide a similar function within the EU, that it is no longer necessary for the UK to duplicate this with their own equivalent of the US Supreme Court.
While the US Supreme Court is often presented as an ideal court, it is in fact representative of the larger problems of the US Judicial branch, namely that courts have increasingly stepped outside of their constitutional role. US courts, including the Supreme Court, are now functioning more as another political branch, yet without the accountability of elections.