There's nothing embarrassing about extending your learning and gaining extra qualifications/a degree.
Thousands of people study with the OU and many of them successfully complete their degree and have no less of a chance at graduate jobs or a good job afterwards than someone who has studied at a "brick Uni".
In fact, it shows maturity to employers especially if you have managed to hold down a degree AND work at the same time. In that sense, you get the best of both worlds; a good education AND work experience, so I don't see why anyone in that position would feel embarrassed!
If people do see it as an embarrassment, that's their choice, but in reality, it's only their ignorance that is embarrassing.