You'd be forgiven for not knowing this because nhl.com is a terrible website and the NHL in general seems desperate to make it as hard as possible for people to watch it, but NHL TV is by far the cheapest and best way to watch, especially if you're in the UK: What You Get (nhl.com)
You can stream every game any time you want. I've used it every season since 16-17, and there have been some problems but it still does what it should. If anything it's better now, blackout restrictions don't seem to apply in the UK any more. I don't know if that's because of how Viaplay works, but it doesn't matter. If there ever are any blackouts they were always easy enough to avoid with a VPN, and I don't think things have changed much. Blackouts mean you can't watch the game for 24 hours after it's shown if it's shown on a channel/network in your state/region/country. I remember that first year, the Avalanche were historically bad and the one game we had on UK TV all year was against Arizona who were the next worst. It was like watching beer league stuff.
The price has come down a bit since then too, I think it was £85 or something for the full season this year. That's every game in the entire league, and playoffs, live or whenever you want. There's usually half season deals too which would/should be going on around now, but again it's not a very well-promoted service on their website so I don't know. You could sign up for a half year subscription at the start of the year which was £49 (I know this because one real problem the service has is the start of the season and renewals being terrible, which had me being charged for half and full year sub this year) but I don't know if that's still a thing or how the playoffs factor into that.
But, aye. NHL TV. Eighty-odd quid for every game whenever you like and a first hand view of the worst designed online store you've ever seen. I recommend it.