UK has changed it’s guidelines to allow people to get a different vaccine the second time around. The CDC and the companies don’t recommend it and are not sure if the second shot will even help.
Our state has a mix of two different vaccines and is giving out a vaccination card with the date needing the second dose and which vaccine you got.
Vaccines are trying to elicit an immune response. In theory it shouldn’t matter which vaccine you used or if you mix them.
However when they are tested for safety and efficacy they are never mixed
It makes perfect sense why the manufacturers would warn against it.
The reason they do it in 2 doses is to get the immune response started on first shot, but not have a big cascading immune response, the the second shot increases the bodies response but should be strong enough by then.
It isn’t a new thing really.
No its not, I remember as a child in the sixties that some vaccinations required a second dose sometimes called a booster shot.
Not exactly though. Some of these vaccines are creating responses to the covid virus’s spikes (mRNA) vs the whole virus (viral-vectored). So there could be variability in exactly what the immune system is being given as a prompt to attack, even if the end result is that it kills the same virus. If the body is given a new prompt, it may not have the same effectiveness as two doses of the exact same prompt—it certainly cannot be assumed that efficacy will be as good as with the tested approach.
What this boils down to is that Britain is guessing that these new U.K. guidelines will be “effective enough”. But they don’t have any data yet to prove anything one way or another.
My perspective is that the correct answer to the question of whether this is a good thing to do is, “We’ll find out later”. 
You don’t have to look back in time for examples. From personal experience I can tell you that current vaccinations for shingles & pneumonia require two doses.
I got my first dose of each back in October of 2019. I was supposed to get my follow-up for shingles in May 2020 but didn’t go in because, you know, CoVid.
My next visit to my local VA clinic was not until October of 2020 for lab work. I used that as an opportunity to complete my vaccinations. I was vaccinated for flu and also with the follow-ups for shingles and pneumonia.
That second shingles shot was many months late. I have no idea whether that makes a difference or not. But what ya gonna do? 
Yes I realize this, I was making the point that the concept goes back quite some time.
The problem to me seems, it’s a different carrier system to elicit the bodies response to the protein. In this case they have decided two doses is better. How much better? Maybe that second dose is just making sure your body knows to respond.
It could even be that two different vaccines are even better, who knows. Like irrational_John has said “We’ll find out later”.
Exactly. We don’t know because it was never tested in a study.
We will know how the britts fare if better worse or no difference.
I do wonder why they chose to do it this way though.
@Timothy I think if you combine the fact that they are having a huge issue like the US with a huge increase of cases. Then add on the fact that they have discovered the new more contagious strain. And then their health system was already struggling with financial costs before covid. Now with the added costs of covid I’m sure it’s an issue.
Then I gather (most?) people didn’t know which vaccine they ever got from the onset, so now they are not sure how to handle that anyways.
Now they are thinking about giving a half dose so they can vaccinate more people faster.
And UK is pondering giving only one dose to vaccinate more people.
It’s generally really safe to give half doses of vaccines without losing the effectiveness. I do this all the time for my animals whether it be puppies, kittens, goats or large livestock.