This was highly embarrassing though I doubt it changes the equation of nuclear deterrence. Even if only half the trident are functional, no nation in its right mind will want half of the UK ICBMs heading their way. Even if you think you can shoot down most of them. It only takes a handful to flatten your largest cities.
The UK Tridents currently are on patrol with 8 missiles (they can carry more). What we don't want is someone thinking that out of the 8 a few won't work and maybe the missile defences around their capital city could surely shoot down the remainder?