I hired a car in the UK for 2 weeks last year. I used Hertz, but only because I had to pay age surcharge, and Hertz was the only company I found that stopped charging it after 10 days. It was still more than half the total cost, but any other company would have been significantly more expensive for me just through the surcharge. Fortunately I am over 25 in a few weeks and the days of age surcharge will be done!
I booked the second cheapest tier available, mainly because the cheapest didn't have air-con. In June, I was glad to have it. It was a diesel Seat Ibiza, manual, tons of space for one, and would be fine for 2.
I used my phone as a GPS, it worked great. Just make sure you have a car charger and a windscreen mount if possible. It tracked live traffic conditions and keeping me off motorways if they were busy. I did find it sent me down a lot of crazy narrow single lane B roads with tall hedges, which were not great to drive down. I also had a large book of maps which was good for planning.
I can agree with previous posters, England is so small and easy to get around, I kept getting early starts planning on driving for quite a while only to have hours and hours spare to do things.
I picked the car up out of London, you could consider taking a regional train out to a smaller town and pick the car up. The trains are really easy and work well, so it might be worth considering.
I really enjoyed my driving trip, hope you do too.