Countries that are able to generally build their warships domestically because doing so employees local workers and companies as well as the domestic defense sector. When you purchase foreign equipment all your helping is the foreign companies and employees producing it. Canada and Australia have the docks and technical capabilities to produce their own frigates and destroyers so why would the want to buy from the UK?
The equivalent question is why didn't the UK just purchase an aircraft carrier from the US rather than building one themselves?
That takes me back. The first timeline I ever did was an improved Royal Navy where CVA01 was followed up by 2 Nimitz class. IIRC they were built in Britain, but buying them from the USA with an offset package would probably have been cheaper for the USN and RN. That was about 30 years ago and decades before I knew about the ASB.
To be serious...
The Australians did buy 4 American built patrol frigates after they cancelled the DDL project. So the way in for the British yards would be to offer 4 Type 22 or 4 Type 42 in place of the Perrys. Apart from the 3 Adams class destroyers the RAN was still predominantly equipped with British built ships or British designed ships. Things were changing by the early 1980s but that wasn't what stopped the purchase of HMS Invincible, which was cancelled for other reasons.
I think the problems are:
1) Not enough Type 22 or Type 42 were being built for the RN for some to be diverted from the RN production line for export. E.g. only 6 Type 42 had been ordered up to 1975 and only 6 Type 22 were ordered between 1974 and 1979.
2) The Type 42s took an excessive amount of time to build due to the inefficiency of the shipyards and the late deliveries of components. If the first 10 had been built in the specified 3.5 years each instead of 5-7 years.
If the British economy had been performing well enough to allow at least double the production and/or building times had been reduced to a reasonable length - then the it might have been easier to sell 4 ships to the RAN in place of the Perrys and then order 4 replacement hulls for the RN. Then the Australians would build more ships of the same design in their own shipyards in place of the 2 Perrys built in Australian yards and the ANZAC class.