I got a job in the UK, but I haven't graduated yet

I have accepted a position for a job in the UK that requires a master's degree.  I won't graduate with that degree until May, but my employer is in the work permit application process.  Although my employer knows I won't begin my job until after I have graduated in May, will UK immigration require proof of the degree in order to issue the work permit?  Does immigration actually require the employer to submit physical evidence of my qualifications along with the application?

I had to provide documentation.  Your work (or you) will need to contact HO to find out if they require the documentation (your app may be approved without the masters, if your case is strong enough).  If they need it, your work needs to wait.

Do you mean you have completed your Master and you're just waiting to graduate? or that you haven't completed it yet? If the former, can you get a transcript of your grades or similar from your university? That might suffice.

I have about 5 weeks left until the end of courses, but this position is in a specialized field that requires a very specific skill set.  I'd think my work experience plus bachelor's would suffice for work permit application purposes.  The only problem is that the job description requires a master's degree, so I was a little worried that immigration would see that and require the applicant to also have a master's degree.  For now, my employer is submitting my bachelor's certificate  and  other supporting evidence (resume, etc.), so we'll see if that's enough!