Auto trader comes up with 52 electric vehicles under £5k nationwide. Most of which are Nissan Leafs. So you’ll be lucky to get 50 miles range out of it. (I’ve mentioned previously on this forum about my work having a Nissan electric van which can barely make it from Oxford to Slough on a full charge).
However given statistical there's 8 trips a year made by people which are over 50 miles there's still plenty of people for whom such a range limit wouldn't be an issue, especially if the vehicle is a second (or third) car in a household.
Anyone aiming to run a car for anything less than about £2,000 a year (where the average is over £3,500) is likely only doing so by keeping their milage low (those figures include purchase price). As such they are likely to be doing comfortably below 8,000 miles a year (8,000 miles is 38 miles per working day, assuming 5 days a week and typical leave allowances, and zero other travel).
Whilst that would require charging every night and it's using 76% of a 50 miles range; it's likely that they would actually get used less than this so wouldn't be an issue.
While you are sacrificing flexibility when compared to a low cost ICE, you are likely to save money and quite likely have a vehicle which doesn't need replacing as frequently. For some the flexibility isn't of value, for others not having it will be a deal breaker, many will be somewhere along that line. It's certainly not something which will work for everyone, but it doesn't need to.
As more EV's get to that sort of age the standard of EV for that price point will generally improve over what's currently available (5 years ago there were far fewer EV's than there's are now). Whilst it's hard to know what it will look like in 7 years time it's also true that things will be better for buying cheaper EV's than it currently is.