Leigh Day are excellent but be aware that they are a big firm. I am a medical negligence lawyer (not affiliated to any firm at present due to parenting and house renovations!). My advice is to go to a larger firm, it will not affect the service that you get.
If you contact AvMA they will give you a list of firms to contact in your area and they will also be able to give you some initial advice. I would phone at least four different firms and see who you like best.
I should explain that AvMA (Action against Medical Accidents) are a charity advocating patient safety.
Good luck. I hope all goes well.