Pretty sure you’ll be an unusual customer, most people are aiming to rent for either short term, <14days, or much longer, ie year+.
All the websites for places like hertz etc are geared up for very short term rentals, ie <14days. It would be worth ringing their national number. Also worth popping in, I know hertz (prob others too) have flexibility on pricing, but only if you talk to them not go via the web.
Not an expert at long term, I only ever do <7days, but my guess is that from the big companies you’d be looking at £10+/day. Interestingly, lots of that is insurance, and I believe (though not done it myself) that you can get separate insurance. Think moneysavingexpert is worth a browse.
Also think outside of the box, know any friends with a spare car on the drive etc. And definitely worth considering buying.