We moved into our first unfurnished property a few months ago and it was a struggle so I feel you. We bought ourselves a sofa bed from Ikea for the living room as we thought it was super practical because not only a sofa but somewhere for guests to sleep. We bought the same one our friends have that we've stayed on a few times before so we knew it was comfy and good quality. My parents lent us the money for it and we are yet to be able to pay them it back
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Argos is great. We got deep-set bookcases from there that are great, important for us as I'm a student so have lots of books and folders and things. We also have a lovely big lamp from there.
Wilkinson's is also great for household bits. We bought cheap plastic foldy chairs from there that we use as dining chairs.
British Heart Foundation is amazing. We got a wooden double bed from there (brand new), a matching wooden bedside chest of drawers (also brand new), and a tv stand unit (used but fine apart from a few scratches).
Look on Ebay too. We have a little glass side-table from there that was very cheap, and a huge shoe rack.
We got a Beko washer-dryer as we live in a flat so it makes it much easier for us to do our laundry as we wouldn't have space for two units and this means we can dry our clothes much easier, we got it from Curry's in the sale.
John Lewis is often pricey but do great long warranties on things and often have offers/sales on. Our telly is from there and so is our mattress.
Ask friends/relatives if anyone has anything they don't need. We have loads of stuff from my parents. They have a large house and are quite well-off so they had lots of things they didn't really need or use anymore and gave to us. Our dining table is from them - it's only a little round table from Ikea and was just sat in their garden shed. We also got a chest of drawers from them that was in their box room with hardly anything in, and a little foldy desk that again was folded up and in the box room. And we've had tons of little bits and bobs for the house from them too.
Asda is also good for cheap bits for the house, and sometimes Lidl and Aldi but it depends what they've got in. We have a little plastic chest of drawers for the bathroom from Aldi.