Landlord is selling house, wants us out before the end of our contract

Hi guys,
I'm in my final year of uni and live in Waltham Forest. Our landlord told us a month ago that she has been told she needs some license that she doesn't have to be a landlord. She said she decided to sell the house but that we shouldn't worry as it will take a year to sell.
Some people from the council came and spoke to her in our house and said we can't be evicted because of the fact that she doesn't have a license.
In the past month we've had people in the house to survey it, an agent came twice and took photos (for which we were told to tidy, clean and declutter the house so it basically looks as empty as possible), the landlord herself has been around a few times too.

She told us a few days ago that someone is interested in the house. They came to look at the house today and are apparently keen to buy. We've been living in the house for four months and the landlord says we'll probably have to leave in about two months. Our contract ends in September. I've read somewhere that she's allowed to evict us after 6 months of living here, which will be the case in two months. She said she'll be serving a section 21 notice. Also we've just paid our rent for another month but we're unsure whether we should be doing that if she doesn't have a license.

I just cant' be looking for a new house and moving my stuff and settling in to a new place in the middle of my final term at uni. I'm already struggling enough as it is with depression and severe generalised anxiety disorder.

I don't know if this makes a difference but at the moment our ceiling has been constantly dripping water for the past few days, 40+ litres in total. We don't know when anything will be done about it - was supposed to be today. We also didn't have smoke alarms when we moved in, they were installed 3 days later. And we've generally had a few problems like this so far, but when I tried to stand up to her about it she came to the house and gave us a speech about how nice she's been to us and given us a shower head (house was agreed to be furnished) and gave us a new front door (previous one had a massive dent in it) etc. and I'm scared to say/do anything again until I'm absolutely sure I'm in the right.

TL;DR - can landlord evict us before the end of our contract to sell her house?