Presumably your first degree is an LLB?
Not sure a master will help you by rectifiying the 2:2, but it adds a little to your CV.
A masters is hit or miss, so whatever you do its a gamble. You will have to check with the firms you are interested in whether you can still apply if they have a min 2:1 requirement..
To answer your question, then theres nothing stopping you, except finance and time.
Whether it will significnatly improve things is very hit or miss.
Your MA can be anything, but they may query what led you to choose whatever it is , when or if you are interviewed. I'd make sure it was something useful.