I applied for a PhD project with a start date of Feb 2021. I was invited to interview in mid January and I thought it went well. I've not heard back from them - its been over 3 weeks. I sent an email to the admin team asking when I will hear the outcome of the interview but have not had a reply yet.
Maybe I should assume its a rejection because its after the start date?

Has anybody else been in a similar situation or have anyadvice?

After an interview, it is customary to get a response either a rejection or an offer. I would certainly ask them until I get a response or may be email one of the supervisors/PI instead to know the interview outcome. Sometimes they go further and give you some feedback on why you have not been selected on this occasion.

Hi,
I second PhDhere. In the UK, you should expect to receive a response, regardless of the outcome. As far as I know, you always get a response. In other countries, things may be different but you should be able to contact them and ask them, just to know. I would suggest that you email the person you were in contact with if an outcome has been reached. I am assuming you were in contact with the departmental secretary who has been arranging the interview? If that was the case, I would contact them. If not, I would get in touch with whoever was in charge of the arrangements. If you get a negative response and they say that decision has not been made yet, I would ask when they expect to finalise it by. You can explain that you are very interested in the project and you are eager to know the answer. If you are, you can also say that you are evaluating other opportunities you have been offered and were particularly interested in their project.
From my experience, decisions often take longer than you would hope and answers sometimes get 'lost' along the way. I don't know which field you are in but I sometimes had to wait for months for a reply on an application (and it was not always because I had been rejected!).
Best of luck!

Having been on both sides of the interview table;

Not getting an immediate offer (within 24hrs), means either:

1) The person in charge is following HR policy correctly, and not phoning you an offer (it's 50/50 on this; many academics ignore HR policy to give an informal offer right after the last interview, as it can otherwise mean days of waiting for HR to deliver an impersonal phonecall, and risks losing the best candidate;

2) You're 2nd or 3rd choice, and they don't want to formally reject you in case option #1/2 falls through.

Beyond 2 weeks, it's sadly likely you've not got the post, and HR have failed in their responsibility to inform you - but it's still possible if you're #2 (or #3) and #1/2 is in some kind of protracted negotiation. Usually an applicant is offered a week to make a decision. So best not to burn bridges in any follow-up.

In any case, you are entitled to send a gentle email asking for feedback. If they confirm a negative outcome, I would still gently press them for feedback, as in my view anybody who takes the effort to apply deserves it, and any academic worth their salt will happily give it (and you may be able to read between the lines on it, e.g. "does not know enough about the X programme at this University", is often code for 'it was stitched up to an internal, but we had to advertise due to policy, and your application was really good - sorry'). In any case, you should always press for feedback as it will improve your future applications, and - contrary to some beliefs - will always be seen as a positive thing by the academic asked to provide it.

Thank you all for the advice.

I contacted them again and got a reply. I was rejected :( The other candidate's background matched the project better.
Guess I'll keep trying.

Don't be disheartened - as I said "The other candidate's background matched the project better." could also be code for 'I appointed my own PhD student/colleague' - because their background would, predictably, match it quite well...

It's about 1/20 on a postdoc application. Stats would suggest hitting at least 14 rejections before getting very introspective. It sucks but from experience persistence pays off :)

Hi guys, does anyone hear anything back after a week but still get the offer?
I read a lot on the internet that if they did not hear back after a week from the interview day, then the most chance is rejection.
Thank you guys