Hmmm...I think your budget will be the deciding factor, honestly.
I own many .223's. Savage Model 10, Tikka Varmint, Howa 1500, a half dozen AR-15's, and I'm probably forgetting at least one.
They all shoot well. Where the difference lies, is in fit/finish, as well as feeding.
The Savage is a tack driver, but it feels a bit clunky. And even with an Accu-trigger, while they can be tuned to be light, the issue is the triggers wear over time, so you'll end up having to re-tune it. It's just the nature of the trigger design. It won't inadvertently fire (by it's very nature it can't) but will begin to happen is when the bolt is run into battery, the sear will slip and be caught by the safety. Forcing you to reach up and lift the bolt handle to re-cock the rifle and slowly lower the bolt handle into battery.
The Howa I have, is also a tack driver. But the barrel twist is the older 1-12, so it was relegated to 40gr bullets for vermin. That being said, it was a slick and smooth feeding rifle from the internal magazine. Nice fit/finish, but the trigger was a bit mushy when you tried to take it down to less that 2.5lbs.
AR's I won't address, since those are fairly rare in the UK.
The Tikka Varmint has been my overall favorite. Primarily because there is a rapidly growing aftermarket support for the rifle, allowing you to customize it to whatever your liking might be. But beyond the aftermarket support, the bolt (with a swept AI style Sterk bolt handle) is probably the smoothest, most silky action of the ones mentioned. It's effortless and flawless in feeding (sitting in an MPA BA Comp chassis with AICS pattern mags), and has shoot many a target and vermin at long range, running 55-77 gr bullets. It's just a real pleasure to shoot.
So I would recommend in the order of highest to lowest:
Tikka Varmint
Howa (Miroku)
Savage
I don't have much experience with the Bergara rifles, save what I see at our local range and matches. They seem to be a good quality rifle ass well though....
View attachment 324719
MPA BA Comp Chassis, Sterk Swept bolt handle, MDT AICS .223 mags, KRG Midas two-stage trigger, Leupold MkV 5-25 TRMR 3