You're not going to get anywhere by threatening him.
I realise that's your DH rather than you, but you can't threaten your kids and expect a good outcome. Even if he does as your DH wishes now, it's storing up a world of resentment for the future.
Blackmailing your child is just wrong, no matter how good the intention behind it. Sooner or later it will drive a wedge between them that will never be made right.
I can see why your DH feels this way. I'd want DS to make the best of his opportunities too, but you can't force him, and especially you can't blackmail or bully him. The worst outcome of that will be him going to the local uni and moving in with his girlfriend and her mum to get away from you. And possibly still splitting up with her down the line but with the damage to your relationship with him already done.
The best thing I can think of for your DH to do now is apologise. Speak to your DS as an adult and explain that he has a chance and an opportunity that not many people will ever have.
Explain that DH reacted badly out of worry and concern, remember that's not an excuse, and explain why you feel that Cambridge is the better choice.
Reassure your son you will support him whatever he decides and tell him you want him to go on in his life with no regrets, and that regardless of what happens in the future with his girlfriend, not choosing Cambridge may be a regret.
Tell him if he choses Cambridge that a long distance relationship is possible, offer to drive his girlfriend to visit him there as often as she likes if that's what it takes to convince him to go.
Remind him that it's an opportunity for her as much as for him, and that many couples make sacrifices in the short term because they know it will benefit them both in the long term.
DH and I do it, we live apart in the week because it meant we could buy our own home. It's not ideal, but it's right for us and we make it work. We're closer because of it and it's an opportunity we wouldn't have had if we didn't make the sacrifice of living apart for a while. It's not forever.
If they stay together then that's fine, you will still have been supportive of their relationship, if they don't, at least he may be at Cambridge when it happens.
But the only way you will convince him to go and not ruin your relationship with him is to make the choice easier for him. You won't do it with anger and blackmail. And if it's based around his girlfriend, promise to do everything you can to make sure they see as much of each other as possible.
And if he still choses to stay put, you're going to have to accept it, even if he comes to regret it. And be supportive if that day comes. You don't have any other choice really.