I would look up all the clinics in the phonebook and call and speak to physios to see what kind of experience they have in treating these kind of symptoms. Maybe an internet search would yield some results. What many people don't realize is that within the profession of physio there are many different philosophies of treatment. For example for your symptoms a physio who follows the McKenzie approach may choose an entirely different plan of care than someone who is Maitland trained. That's not to say that one approach is necessarily better than the other. I believe that there may be a number of different ways to treat a particular condition but it is important that the patient is diagnosed correctly.
When calling ask what percentage of the patients they see are lumbar spine patients and the number of years experience the physio has had in treating these conditions.
Forgive my ignorance but is the nhs some sort of government setup in the UK? Anyway a negativeMRI does not mean you don't have a lumbar spine problem. An MRI is just one piece of the puzzle. A solid clinical evaluation(ie interview followed by hands on testing) should always be the primary driver in determining the plan of care from a physio perspective.
What you're describing could indicate a lumbarradiculopathy ie impingement of a nerve root in the lumbar spine which is causing muscle weakness. If you find someone who can test for this, along with a comprehensive look at your back, pelvis and legs, and then treat you appropriately you may well find some relief.