If I've got my facts right, what they've done with 'overlooking' him is fair - employment law does not include any entitlement to promotion, nor any requirement to advertise roles publicly.
Employers can employ who they want without opening it up to others - except in a situation where there are people under notice of redundancy (ie: have had an 'at risk' letter or a redundnacy notice) in which case, anyone transferable to an equivalent role has to be offered the role (if there is one job and two suitable candidates under redundancy notice, then both are supposed to be given the opportunity to apply.
Your DH was not under notice of redundancy at the time the new guy came in, so that is not applicable here.
A redundnancy scenario only relates to where the work done is no longer required. They can't actually make him redundant, and employ someone else to do the same work. If the work exists, then his post exists, he is the postholder and he would therefore have a case for unfair dismissal. Unless there is a restructure taking place, which it sounds like there might be ie: rolling of work into another person's role.
With the limited information you've provided, my questions would be:
Is the meeting that has just happened considered a 'redundancy consulation' where he has been told specificually that his post is at risk.
What is is his legislative period of notice (and if different) what is his contractual notice period , based on time served.
What is his contractual redundancy pay due, and his statutory redundancy pay due (if different)?
I think if this does come to your DH's role being made redundant, I would be looking at appealling and asking for how they came to be making his specific role redundant.
DWP site
I think they could argue that the job your DH was doing no longer exists, as it is now rolled into someone else's role. Or that they need to cut costs, so they need to cut staff numbers.
flowery will be able to help, I expect.