Not as bad as you think.
You're overestimating its power. By default, a point of crit chance is actually a little bit less valuable than a point of to-hit. +1 to-hit means that 1/20th of the time, you have a moment where you would have missed (doing no damage) and instead hit, doing full damage, plus any secondary effects that may apply. +1 to crit means that 1/20th of the time, you do a bit less than twice the damage (dice are doubled, but things like the damage bonus from stats is not), instead of doing full damage, and you get unchanged secondary effects. Also, there are things out there (like, say, humans wearing adamantine armor) that do not take additional effects from critical hits.
Of course, that's overly simplistic. Things like secondary effects on miss, or the paladin's ability to add dice (doubled by crit) after the crit has been determined, or even the rogue's sneak attack, which adds significant dice, but isn't expended on a miss, can all increase the value of crit range as compared to to-hit. Further, if the enemy's AC is so high that it overwhelms the PC's ability to hit on anything other than a 20, having an extra point of crit range means that instead of going from hit to crit, you go from miss to crit, and the bonus to hit wouldn't have helped you at all. Finally, it's likely that the person who winds up with the item will be the one who can use it most effectively. There's a good chance, as such, that it'll be worth a bit more than +1 to hit, rather than a bit less... but it's still in the same ballpark. As such, I'd look for things that give a bonus to hit that aren't magical weapons (as they'll stack).
Answer: there aren't any. 5e has this whole "bounded accuracy" thing that's really very opposed to letting you rack up to-hit bonuses off of your random gear. The closest thing you could get to it... probably a Manual of Gainful Exercise? It's a very rare item that increases strength by 2, which (for a significant number of character types) would effectively give +1 untyped bonus to hit. Of course, it would also give a +1 untyped bonus to damage, it wouldn't take the helm slot or the attunement, and it would give a bonus to strength-based skill checks, ability checks, carry capacity, and so forth. As such, it's clearly stronger, by a fair margin.
Given all that, I'd say your helm is one step down from a Manual, and call it rare. That's a judgement purely from a power/utility standpoint. If you feel that crit is special enough that it shouldn't be handed out at Rare, then that's reasonable to conclude, but you should seriously consider adding something more to it to bring it to the appropriate power level for a higher rarity. For example, if you let the +1 apply to both hit and crit (making it the rough equivalent of +2), that could certainly serve as very rare. If you then added on some useful side powers (say, advantage on Perception checks, and at-will detect magic) it would do fine as a legendary item. If one of your players is expecting a legendary item, though, and what you give them is a helm that gives +1 crit rating and requires an attunement slot... well, it's no Robe of the Archmagi.
