Joie 360 Spin (or i-Spin 360) / Graco Turn2me is probably the best budget one, but it will only fit well if your car doesn't have a strong slope on the back seats. You also need to be fairly confident in fitting babies into it in order to get a good fit, and you are unlikely to get a good fit for a smaller baby under ~50cm (even though they are approved from 40cm).
They have a newer one out now called the i-Pivot which I haven't seen in person, so not sure if it's the same in terms of newborn suitability - I think the inserts might be different.
If you can spend a bit more but still want the spin, Besafe izi Turn B (forward and backward facing) or Besafe izi Twist B (rear facing only; Swedish plus tested) are the nicest spin seats for newborns up to 105cm (approx age 4.5) IMO. This seat is a bit of a beast in terms of weight, but it's incredibly solid and well designed and it can counteract any slope in your vehicle seats. It has to be the "B" version to come with the newborn insert.
I'm not up to date on the current Britax or Cybex seats of this type - they might be worth looking at in comparison to the Joie or Besafe (both of which are stocked by John Lewis among other stores). If you want to assess newborn suitability, see if you can find or borrow a soft-bodied doll or teddy where its body fits into a newborn sized vest, and take this to the shop and ask the staff if you can try it in different seats. They might also have a demo "baby" you can use, although these are often weighted at around 6kg which is roughly the size of a 3 month old. You're looking that you can bring the doll's bottom down to the crotch strap (or wherever it sits on the newborn insert, as some "boost" them up instead) and the shoulder straps are still nice and snug on the shoulders, and also that it's physically possible to tighten the straps around such a small "baby". With some combination seats, the shoulder straps are floating an inch or so higher than the shoulders, which is no good, or you can't fully tighten the straps because the pads which are usually needed for safety are so long that it prevents you from tightening them further.
The other thing to check is the angle that each seat sits at (bearing in mind that this may well depend on your car) and whether the design of the inserts creates a flat line for the baby's head, neck and spine (good) or whether the head is either forced forward or tipped right back - neither of those are good.
It also tends to be good if the newborn or infant insert has bolsters or padding at the sides to help cradle their body while they are still small. And then some seats (e.g. Maxi Cosi Mica) have an issue in that the insert is very good for newborns, but it is very chunky and comes completely out as one piece, so once the baby gets to about 3-4 months and the insert needs to come out, they are totally lost in this huge roomy seat which is a pain. I know that Britax sell a "comfort insert" which is useful for this in between phase. For some fixed seats which are suitable from birth, the insert is a newborn insert which means it is used until roughly 3-4 months, but sometimes it's an infant insert designed to mimic the angle and "contained-ness" of an infant carrier, so should be used up to about 9-12 months. You can check by downloading the manual of the seat in question if it does not say on the insert itself.
Another option is to look at seats which last a bit longer. Axkid One (whichever number but must be "+" version for newborn insert) lasts up to 23kg/125cm which is about age 6. Again Swedish plus tested, and one of the most practical ERF seats on the market due to the rails letting you slide the seat back and forward to adjust between child leg room and front seat room.
Avionaut Sky or Besafe Stretch B are two belt fitted options up to 125cm, cheaper than the Axkid.
Or Avionaut Stardust is supposed to be good as well, that one is pricey, but manages to combine the spin option with an ERF mode up to 125cm and then a high back booster mode as well. I am not sure what to make of this one, because usually I'd say to avoid the "all stages" seats but this does seem to have some pretty good credentials and the newborn fit looks very good.
- Is it important to have a "perfect" fit for a newborn? Arguably no; many infant carrier type seats don't give a perfect fit for tiny newborns. The smallest crash test dummy is modelled on a 6 week old baby, and they grow and uncurl a lot in 6 weeks. If you don't expect to spend very much time in the car in the first few weeks, and journeys are liimited to under 30 minutes anyway, then it doesn't make a huge amount of sense to obsessively optimise for this period.
One more thing to consider - some of these seats have two versions, where the version with the newborn insert typically costs around £100 more than the version without newborn insert, which can usually be used from around 4-6 months, when baby is comfortably sitting with support. (Some models are more for use from 9+ months like the older Axkid Minikid).
So you could, as an alternative, purchase a basic infant carrier for less than £100 to use for this period and then this gives you a much wider choice of fixed seats to move into later. For this price you wouldn't usually get pram compatibility or a base, but you can fit these seats using seatbelt. These are the models I'd look at:
Joie i-Juva
Graco Snuglite i-size
Hauck Comfort fix (does come with isofix base)
Britax Baby-safe core (this does go on the most popular universal pram adapters)
Cosatto Acorn 2 in the clearance fabrics (pram compatible)
Maxi Cosi Cabriofix i-size (pram compatible)