You can apply for entry level positions in Java and at the same time put some effort into preparing your CV properly.
-- Have an objective section and clearly state your intention to transition something like
"I am changing careers from "blah" to Java/JEE based software development and it is my passion in Java/JEE sustains me in this transition. I have gained SCJP
, M.Eng in IT and also gained hands on experience through self-taught and opensource projects etc ........................"
-- Write a CV that highlights your achievements, skills and experience to date.
-- Also brush up on Java/JEE and build some confidence by gaining some hands-on experience through doing tutorials, sample project(s), community project(s) etc.
Employers always look for entry level positions and you need to have a CV that stands out to compete with the graduates.
All the best.