We use Virtuo when we go away for a few days, really nice cars (Merc GLA; BMW 1) that are new and clean. They can drop off the car to your house (or street) and pick it up at the end - again, not for a single day, but we tend to go for 3/4 days. Not the cheapest but competitive and for the great cars - we like it. There is also pick-up from ncp near Guy's Hospital. Here's a £30 off referral https://tinyurl.com/virtuoED if you're interested (yes I get that too).
I recently used Zip car for a daily rental- was more expensive than virtuo rate (though local ED pickup was a plus) - but a 70k mile clapped out MG was a pretty terrible experience - squealy breaks, no suspension, the leather'ish drivers seat threadbare on right side. Surprised any car rental company could keep vehicles on the road that long.