Same here and with a friend I play with, both in the UK. We have both had varying degrees of lag in SP & COOP (but not in DZ!?) where bullets don't hit the enemy until 3-4 seconds after fired. Same thing happens with taking damage, healing & reloading.
Early morning on launch day it wasn't too bad, it got worse yesterday evening and really bad in a COOP game. It behaves like actions are getting queued up if theres a lot going on and are being worked through one by one by a slow server. Healing, reloading, shooting and even movement commands can get delayed while it completes the last request.
Its really spoiling the game for me.
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Just to head off the inevitable "Your internets rubbish, old slow computer!"...
On a skylake I7-k, 970-sli. My in-game frame rates are pretty steadily above 60, occasional dips/spikes down to 40-50. I haven't gone up to the very latest Nvdia drivers as I've got dual monitors but will as soon they fix.
I've done the usual, validated download, checking and restarting, router, connection, dl/ul speeds, nothing else downloading in background, firewall, switched off ASUS gamefirst etc etc. I'm on my own (no one else using) 40mb fibre line thats pretty rock solid, worst peak time dips about 30mb.
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I'm going to try a few things after work this evening and will report back if anything does the trick. The most similar example I have is in Rocket league where after an update, it changed the default server location to Pacfic and my ping went from 10-20 to 300.
Best guess right now is either Ubi servers are slow/overloaded or its connecting some players to the wrong regional servers?
(Helpful) ideas welcome!