Derek Jackson.
For a person wishing to move monies from Briton to Canada in 1938 in the amount you specify the process would have been fairly simple. Unlike other members of the British Empire, Canada while on a fixed exchange rate wasn’t on a one to one rate, i.e. one British pound equalling one Canadian dollar. So what you would have done, is arrange for your bank in the UK to raze ether a cashiers cheque or bank draft in Canadian dollars, for which they would have charged a fee. You would then have taken this with you to Canada and depending on the bank you intended to use there, ether cashed it for cash, or deposited it into an account set up there. Note you could have just taken cash in pounds sterling with you, and again for a fee exchanged them for Canadian dollars once you were in Canada. At this time there were no exchange controls on moving money in to or out off the UK.
In regard to the movement of the smaller amount the other way, it depends on what you want to do. As Dathi THorfinnson has already said, you could at that time have brought a Postal Order, and posted it to the recipient in the UK. While it would have probably cost more to have a Sterling one issued than a Canadian dollar one, I am reasonably sure it was possible. As a young man I used to receive postal orders from New Zealand as Christmas and birthday presents from my uncle out their.
Or you could have arranged for a Wire Transfer, from an account in Canada to an account in the UK. Alternatively you could have brought an international money order, and sent that.
Regards RR.