Here are the top 40 universities in both the United Kingdom (England) and the United States:

United Kingdom (England):

1. University of Oxford
2. University of Cambridge
3. Imperial College London
4. UCL (University College London)
5. London School of Economics and Political Science (LSE)
6. University of Edinburgh
7. King’s College London
8. University of Manchester
9. University of Bristol
10. University of Warwick
11. University of Glasgow
12. Durham University
13. University of Southampton
14. University of St Andrews
15. University of Birmingham
16. University of Leeds
17. University of Sheffield
18. University of Nottingham
19. Queen Mary University of London
20. Lancaster University
21. University of Exeter
22. University of York
23. University of East Anglia
24. University of Sussex
25. University of Liverpool
26. University of Aberdeen
27. University of Reading
28. University of Bath
29. University of Surrey
30. University of Leicester
31. Loughborough University
32. University of Strathclyde
33. University of Newcastle
34. University of Dundee
35. University of Cardiff
36. University of Kent
37. University of Glasgow
38. University of Portsmouth
39. University of Essex
40. University of Plymouth

United States:

1. Massachusetts Institute of Technology (MIT)
2. Stanford University
3. Harvard University
4. California Institute of Technology (Caltech)
5. University of Chicago
6. Princeton University
7. Yale University
8. Columbia University
9. University of Pennsylvania
10. University of California, Berkeley (UC Berkeley)
11. Johns Hopkins University
12. University of Michigan-Ann Arbor
13. University of California, Los Angeles (UCLA)
14. Northwestern University
15. Duke University
16. University of California, San Diego (UCSD)
17. Cornell University
18. University of Wisconsin-Madison
19. University of Washington
20. University of Texas at Austin
21. University of Illinois at Urbana-Champaign
22. University of North Carolina at Chapel Hill
23. University of California, Santa Barbara (UCSB)
24. University of Pittsburgh
25. University of California, Davis (UC Davis)
26. University of Southern California (USC)
27. University of Minnesota, Twin Cities
28. University of Maryland, College Park
29. New York University (NYU)
30. Boston University
31. University of Virginia
32. University of Colorado Boulder
33. Ohio State University
34. University of California, Irvine (UC Irvine)
35. University of Rochester
36. University of Florida
37. University of Arizona
38. Purdue University
39. University of California, Santa Cruz (UCSC)
40. Michigan State University

Please note that rankings can vary depending on the source and methodology used. The list provided here is based on general consensus and reputable rankings as of my knowledge cutoff in September 2023.