Hi, what are your predicted grades? That can help when choosing universities (you can look at UCAS and it will tell you how likely you are to be accepted). The universities you picked are good but it will be better to go to a more competitive university such as the University of Edinburgh and Queen Mary University of London.
The Russell Group universities are generally considered better than the universities you listed (Royal Holloway, City, University of London, University of Surrey, Brunel, and Goldsmiths) because of many top law firms actively recruit from Russell Group universities due to their strong reputation and rigorous academic standards. Graduates from these universities may find it easier to secure training contracts or pupillages.
Russell Group universities typically have better funding, allowing for state-of-the-art facilities, larger libraries, and more extensive student support services. Russell Group institutions often have stronger international ties, which can be beneficial for students interested in pursuing opportunities abroad or within global law firms.The Russell Group universities that don't require the LNAT are University of Edinburgh, Queen Mary University of London, University of Liverpool, University of Birmingham, University of Manchester, University of Leeds etc.