Landlord Worries/Advice

Hello!

I was hoping someone would be able to give me some advice on how best to handle a situation. My partner and I are currently looking for somewhere to live quickly as I start my third year tomorrow (He graduated this summer) because our current living situation has fallen through.

I went to see a flat on Saturday with my mum, and this morning we texted the landlord to say we'd like to take the property. I'm dealing with the landlords privately without any agency involvement.

The landlords replied saying that they still have viewings this coming week, so they will contact us towards the end of the week about the flat. I wasn't sure what to reply to this, but I just said that we hope to hear from them soon and that we really like the flat.

I don't really think that this is normal etiquette for renting somewhere, but I also don't want to ruin my chances of getting this flat by rubbing them the wrong way. Should I say that I need an answer sooner than that, or will that ruin my chances? How would be best to approach this issue?

We really need to know what we're doing as obviously we need somewhere to live asap. Is this normal policy for some landlords? Or is it a sign that the landlords didn't particularly like me very much?

Anyway, I'd really appreciate any advice or support on this. I'd hate to wait all week only to be told that we haven't gotten it, which I have a feeling is what's going to happen.

Thanks so much in advance!