"The UK is a nuclear power, some people don't like this, however that's the way it is even if we did keep our nukes safely under lock and key away with a bicycle lock. Part of this means that we have nuclear submarines patrolling unseen and undetected around areas we see as threats or assets (Yes Argies if you fancy another Belgrano incident come and have a go) Now there is some dispute as to whether or not the nukes we have are actually under American control (as in we can't fire one without their permission) but the subs themselves aren't, nor are they under EU control as yet, though that may be about to change.
"Yes it's expensive, but, considering the fact that many countries out there are developing a nuclear option probably necessary. As even if they manage to disable or take out a land target, they'll never know where or when our revenge will come from, that's the whole point of deterrence. Yet if we share patrols we also agree to take on the interests of the French, whose interests are not and have not ever been in ours. We may share common ground, but we certainly don't have the same world view or same purpose in government. This would leave us having to consult or perhaps get permission to use our forces in our best interests, which may not be in the interests of our EU neighbours, certainly wasn't during the last Falklands war when the Belgians refused to supply us with ammo.
"Personally I think all our military needs should be produced here and under our control, even if made under license, certainly at least the ammo. We should however remove the military procurement regime from the MOD, if we need to buy, let us get the best value for money, if it means buying from abroad (helicopters and the like) see if we can build here under license, but get it here, train our people again in manufacture and keep the EU at arms length on the one part of our sovereignty that allows us to defend ourselves."