I'll go the whole hog on this...
The CF-105 isn't cancelled. Enough are built to equip 25 squadrons on a Unit Equipment (U.E.) of 18 aircraft each, which means 450 for the U.E. plus another 150 for "backing" which is the operational training units, maintenance and reserves to replace attrition for a total of 600. The 25 squadrons consist of 21 in RCAF Air Defence Command (9 regular and 12 RCAuxAF). The Royal Belgian Air Force buys enough to equip its 4 Canuck squadrons. After realising that a massive mistake was made in the 1957 Defence Review, HMG allows the RAF to buy some to replace the Javelin in the first half of the 1960s.
At the same time a specification is issued for a single engine fighter to replace the Sabres in 1st Air Division. However, because Avro Canada is busy with the Arrow, the contract for what became the Quarrel went to Canadair so no R&D or production synergy. However, Quarrel used the same engines as the Arrow. Total production for the first-generation Quarrel for the RCAF was 238 aircraft (200 single-seat and 38 two-seat) to equip 8 squadrons in 1st Air Division, plus the prototypes.
(To please
@Just Leo) the early Quarrels flew like pigs with an even higher accident rate than the Starfighter. And that was when their appalling serviceability rates allowed them to fly.
However, that didn't stop Canadair winning the NATO fighter competition with a sales technique called, "offering bigger bribes than the competition." As a result 113 were built for Belgium, 915 for Germany, 354 for Italy and 138 for the Netherlands. The Japanese also built 230 Quarrels instead of the F-104J. With the Starfighter out of production the US Government was forced to buy Canadair built Quarrels for China (Taiwan), Denmark, Greece, Norway, Spain and Turkey under MDAP or supply Freedom Fighters.
The second-generation Quarrel spent less time on the ground and when it was in the air was less prone to crash landings. The RCAF (no Unification ITTL) bought 135 as attrition replacements instead of the Freedom Fighters of OTL. The Dutch bought 105 instead of their OTL Freedom Fighters and the Belgians built 106 in their factories instead of the Mirage 5.
In the meantime the RAAF had selected the Quarrel to replace the Commonwealth Sabre in preference to the Mirage III.
BAC took out a licence on the Quarrel which it offered to the RAF as an alternative to the P.1154 to replace the Hunter FGA Mk 9 and FR Mk 10. This was offered with modifications to improve its STOL performance and a choice of the original Iroquois engine built under licence by Rolls Royce or the Spey still being developed for the F-4K Phantom ITTL. The Spey-Quarrel won and over 300 were built for the RAF in place of the OTL Harrier Mks 1 to 4 and Jaguar.