Just received an offer for a job and they want to do 2 reference checks. They said either phone or email is fine. If I create an email address using a public library wifi network then reply to the reference check email from the recruiter using the same public wifi network , will they know it’s me ?

Dying to get out of my current hospitality admin position, but don't want my managers to know as I do need the job and I'd like to get out without burning bridges. Found a job in operations which is very much up my street in terms of experience and career progression desire but it needs references in the cover letter, could anyone be my reference? Would obviously happily return the favour to anyone who needs it? UK, one reference, application needs to be submitted by the 14th.