I’d say it’s worth spending a bit more to get one that does, at least partly, replace the corded. The cordless is great for household cleaning, maybe get the corded out a couple of times a year if there is a big mess. All the cheap ones I’ve tried have been pretty wheezy.
You can probably pick up a second hand Dyson well under budget. The battery lasts a couple of years so people give up them, sometimes even for free on Facebook marketplace. It’s an easy thing to replace for about £18
Another option if you have cordless tools is to get a vacuum that uses the same battery and buy a bare unit. I’ve got a Makita and it’s pretty decent, bit over budget though.