October seems very optimistic but it would be good if all the required testing could be done by then.
But of course it will take a long time to carry out an implementation wide programme even if we can secure enough of it for this country. We have around 65 million people in the UK (although maybe young children can be omitted) but at any one time a few million are temporarily overseas and we also have many millions of visitors coming into the UK, plus legal and illegal immigrants, whom we need to cover. I can see that taking a couple of years. And of course there will be many who refuse the vaccine ( a survey showed 1 in 6) plus those who will want to wait at least a year to see if the vaccine has side effects that come to light later.