I agree with everyone saying the one salary would be tight but not impossible. Those saying I manage on £20k- do you not get any benefits/top-ups with kids? I find that hard to believe.
I live in a similar area and the problems are a) lack of rental properties full stop, I just googled Truro rental (Truro is quite desirable though) and there's two, just two three bed houses and both are over £1200 a month, so that's what you would be paying unless you can fit in a two bed b) likely need one or two cars and petrol, this is a lot extra than if you live centrally in a city c) high water rates d) high food prices and very few cheap markets like in the North (which I can't get over when I go there!) e) expensive to buy.
None of this is insurmountable, but most people have either two wages coming in or one and part time or one and benefits or some such combination, very few people these days have one wage and that's just it. I am a lone parent, so I do, but my wage is higher than your husbands and I wouldn't say I'm feeling flush right now.
If moving to be with family is the most important thing, then move once your husband has a job and you then move for work, could you live with family for a little while? Then you can get a part-time job, in whatever comes up.
If lifestyle in terms of eating out, takeaways and generally not having to be too worried about money is important, like having the heating on a lot, then that's not enough on his wage alone. With two of you it's a lot better, and would give the wiggle room for the extras that make life a bit more bearable (not stressing if something breaks, kids going on school trips, odd meal out somewhere reasonable, holiday once a year, treating the kids to stuff).
Sorry OP, but there's been rampant inflation and 37k isn't what is used to be. Those saying it's the average wage are not comparing like with like, or are saying not eating out ever or having a takeaway is fine. You just have to know what's most important for you.