What shall i do about this guy who fancies my g/f?

Maybe report him to HR. What other answer do you expect from strangers on the internet? Or maybe you're reading into his alleged actions and demeanor? Then go to see a therapist and talk about your possibly toxic jealousy.

HR have spoken to him (Apparently) but my company likes to sweep things under the rug.
He is a coward as he is quiet and walks away whilst I’m there.
I do believe he is jealous.

Since he won't talk to you it's really under your girlfriend's control. She can handle it more effectively than you can. Workplace relationships can be tricky.

If he's just talking, who cares? Why are you concerned about this? People are allowed to talk to one another, you know. What's the big deal?

And what's "this guy who fancies my g/f" have to be jealous about?

Yeah, that doesn't make sense.

It is not talking which bothers me or having a laugh it is the crude/offensive things he is saying to her which is annoying.
My girl friend is 25, I do not say crude or offensive things to people or to their partners. If i met his partner i would never try to hook up with her or say crude things out of respect.

That is the impression I get as when me and my g/f chat or hug etc the guy walks away red faced and muttering under his breath.
Or if i catch him saying something crude/offensive I say what was that comment he goes bright red faced and walks away looking down muttering.
I would never say anything crude/offensive to anyone.

This is the first time you mentioned the comments were crude and offensive. Can she not complain to HR about him? They should know. She should file a formal complaint - that's sexual harassment.

I should have mentioned they were crude comments. We have told HR they have told him but he still does this i said report him again.

Document the comments (along with names of third party witnesses). Consider hiring an employee attorney if HR refuses to intervene. Or consider going to a local regulatory entity that covers employment law/ordinances in your city/state/etc....

If you can join a trade union.

trust your girl... you can't stop men from oogling her and she has to decide when it crosses the line. trust her. women are way better at handling idiots than we men are. When it's time she will go to HR. If she doesn't, then talk about why. it may be deeper than and more significant than your male mind can think of. bottom line, trust if trust is warranted. be there for her.

Chill out. It's up to the GF to sort him out.

If his girlfriend is being sexually harassed at work, and HR aren't doing their jobs properly, it's a bit more serious than that.

IF. He didn't say she was or that she says she is. HR didn't act as if she were. I'm more inclined to see a controlling boyfriend.

This is an issue the GF needs to deal with and needs to be addressed by HR who have already looked into this.

We agree: it appears the GF is uncomfortable with the situation, but to me it seems not as concerned as is the BF.

I just don’t like people disrespecting my GF like the way he is.
HR at my place sweep everything under the carpet all they said was to watch what he is saying to the females at work.
They didn’t talk to people who were in the room/witnesses as soon as we told HR about 10 mins later the guy got called in by HR.
She has been in tears over his comments.
My GF goes out with her friends I’m cool with it some are male and some female.

In the workplace she has to rely on HR. You, nor she, can do much directly...nor should you. If she has denied his overtures and reported him to HR, then the company is on the hook deal with it. If they don't, then SHE has to take the next steps. HR is required by law to investigate and disposition the "claim". She has to work this out with the company. Otherwise, she has to go to the police and log a complaint of harassment and then it becomes a civil lawsuit.

If she is facing legit sexual harassment, there are no ends to your legal recourse. Just be certain you and your mate are true to your word and the situation. HRs don't f around in legit companies. No owner wants to be sued, they act immediately and with legal prejudice. If it's a large company, they will be taking it very seriously.

My point is that I know for a fact that large companies don't f around with this stuff. It's serious and HR will deal with it. If it is a small company, I'm not sure, but she has recourse. It's not great, but she has it. Not saying it's her fault at all.