What makes you say that. For Economics as an example, the targets are in the top 5 in the table excluding st Andrews so surely the tables are pretty accurate. The same applies to the top universities for Law which are all in the top 10. I'm worried now.
Instead you should be picking your uni based on how employers view the Econ/Law departments. Firms don't use the league tables to hire grads, city recruiters already know which universities produce strong grads. This is why I really wouldn't be worried if your uni moves down a couple of places. I'm not sure which one you're referring to but I really recommend you to look into the league table methodologies if you want to stop being worried. You'll realise how useless they are and hopefully that'll settle some nerves.
With regards to how good the Econ/Law departments actually are at teaching, how rigorous the courses are and how well they place grads into good jobs, I'm afraid can only speak for economics. Nottingham is in the group after the top5 so is broadly ranked 6-9th. Manchester (I'm assuming BSc?) Would rank in the next group, broadly 10-15th. Birmingham is lower, maybe 15-20th.