I've had the privilege of staying in 5 London AirBnBs this year, ranging anywhere from 2 nights to 3 months (I stayed in Jess & Tim's place 10 nights). Of these 5 AirBnBs, 3 were amazing/excellent, 1 was ok/pretty good, and 1 was terrible (think non-working bathroom for multiple days). Jess & Tim's place is the 'ok/pretty good' one.
Why? Well, first let's cover the positives: 1) great central location - near buses (around the corner!), tube stations (10-12 min walk), markets (2 just around the corner!), and great eateries, pubs; 2) nice layout/design of the space with even a cute, little private balcony; 3) great modern and clean look of the kitchen and bathroom; 4) Jess is very nice over email; and 5) the price is fair for what you get.
What are the negatives? Well, a few days before I stayed at this AirBnB I read some recent reviews and one mentioned the furnishings look more drab in real life than the pictures suggest. I was really, really hoping this wasn't the case, but unfortunately that review was accurate. A little TLC would go a long way for this AirBnB. New balcony chair cushions, new sofa pillows, new bed pillows are musts, some more drinking glasses (only 1 real glass, the rest were wine glasses), the blinds in the bedroom also need to be replaced (almost half had fallen and were left behind the curtain on the floor). Also, the bottom bedsheet had two very noticeable stains on it, so a company that uses nicer linens would be a plus. (Oh, and the apartment wasn't clean at check-in time either; I had to wait an extra hour and a half for it to be ready.) The owners live out of the country and it doesn't seem that they use a property management company, which is why things like above or other things (like the slowly draining bathroom tub) are likely to occur. Another negative that I don't fault the owners for is the noise level. There is a tiny playground right next to this flat, so if you don't like children screaming in the afternoon into early evening, beware. Also, in warmer weather there is a lot of congregating in the nearby streets and buildings at night, so noise levels are high until just before midnight. In chillier weather, I suspect this flat would be really quiet. I noticed when it rained it was serene and peaceful.
I hesitate to even write this review because I completely wanted to love this place, but overall it was just ok/pretty good for me.