I would have found 6 weeks unspeakably early, a real wrench. I would try to think laterally about this.
Firstly, babies don't need their own room. In fact the SIDS guidance is that the baby should be in the same room as you for 6 months. When DS was born we lived in a one bed flat in London, and we were there till he was 18mo old.
Then once we moved to a bigger place, he was still in our bed till he was 2 years old. That doesn't suit everyone, but just to mention it.
In fact, especially if you're a single mum and if you plan to breastfeed, it could be worth giving co-sleeping a go. When babies are little, they just want to be near you, as well as wanting milk. That's what a lot of night waking is about,( in my limited experience!). The bottom line is that you may get more sleep if you can just roll over to comfort your baby, and the baby can get comfort and milk instantly, rather than having to wake him/herself up, enough to wake you up down the baby monitor. Often there is a merry dance about who gets to sleep in the bed, with sometimes the DP being kicked out while the baby is young, or the baby in the next room and the mum dragging herself around in the middle of the night. If no DP, great, as far as that argument is concerned! You and the baby can get on with it without having to take anyone else's needs into account.
Your HVs will warn you against co-sleeping, and it's a judgement call whether you want to do it or not. There are stats to show that co-sleeping is riskier, but they generally include things like people sleeping on sofas with babies (very risky), drunk people sharing their bed etc etc.
If you don't fancy bed sharingm, you can co-sleep by getting a three sided cot (there's a good one, about £110 incl postage from Germsn Amazon). This will keep the HV happy while giving your baby and you easy access to each other.
Sorry a bit of a ramble! But my basic point is you need to look at ways to change things so you can fit a baby into your life without sacrificing things you may not want to (e.g. Time with your baby).
So a 1 bed place for now would be doable, if that helps? Or a two bed and getting a lodger in, as suggested above.
Also, any chance of movng nearer to family and friends, or the father? Having a bit of support could be a great help.