Covid-19 Vaccine History Lesson

The Government have told us not to get our hopes up about the Pfizer/BioNtech Coronavirus vaccine as it is still in the trial stage but they are very confident that when it does come, it will work and are so confident that they have set in place the infrastructure to inject all 65 million of us with the first recipients being penciled in for December.
The 3rd stage trial has injected 43,000 people and no safety concerns have been raised and Pfizer have said that it will be able to supply 50 million doses by the end of this year, enough for 2 doses for 25 million Brits, which lines up with the Government's December but there is something in the back of my mind which doesn't seem to sit right.
We have been continually told that due to the strict testing required, the vaccine would not be ready until summer 2021 and now suddenly it is to be ready by December 2020 which means that either the original targets were way off, or the testing period has been made shorter than normal and that concerns me.
BioNTech scientists have been saying that some crucial questions regarding the jab’s efficiency will only be answerable in the coming months and establishing for certain whether it can also stop asymptomatic infections could take up to a year, they are not even sure how long the immunisation will last once the vaccine has been taken.
Vaccine's work, the eradication of small pox and polio prove this but we have a devastating example of when a medicine has not been properly tested, Thalidomide.
In the 1960s, Thalidomide was deemed a wonder drug and despite sparse testing and never being tested on pregnant women, was prescribed as a cure for morning sickness.
After a large proportion of children were born with physical and psychological deformities, 40% of them dying before their first birthday, it was withdrawn and the disaster prompted many countries to introduce tougher rules for the testing of drugs.
The Medicines and Healthcare products Regulatory Agency (MHRA) have reassuringly announced that any Covid-19 immunisation will not be released for use in the UK until it passes final safety tests and they are satisfied enough to give it the go-ahead, stating they will not be pressured by the Government to lower its safety standards despite the need to get a vaccine quickly but it still concerns me that this is being done with too much haste.
I get that with the UK government announcing another 24,962 confirmed Covid cases today and a daily death toll hovering above 400, haste is required but the drastic reduction in the time needed to properly test it, coupled with a Government who are no stranger to duplicity, it does bother me because any problems discovered afterwards, if there are any, are going to be too late.