(ROUGH RULE OF THUMBS CAVEATS ALL APPLY).
Basically, salaries are (generally) lower in the UK compared to the US, for the same job and same experience. Approximate figures for other jobs: starting salaries for first year magic circle lawyers: $180k USD, £50k gbp, starting salary geologists in large operators: $90k usd, £36k gbp.
My general point is that an "absolute" conversion rate would be roughly around 3 between US and UK. Not sure how that compares to Canada (convert Canada-> US -> UK). So maybe that will help you figure out what is typical of project managers. Unfortunately I don't know much about construction or project managers, but £37k gbp with 3 years experience sounds in the ball park.
Anyway, some things are cheaper (fuel and transport -- don't need a car! you can get by with public transport), groceries are incredibly cost competitive as supermarkets here face huge competition, you can feed a person very good food and fresh veg for £80 a month, but the major sticker shock will be housing. Check out Moveflat, Zoopla, Rightmove for an idea on rents. 1 bedroom flats will be in the range of £1000 and upwards for a decent commute (<40 minutes door to door).