We spent a happy month at Lawrence's apartment (June/July).
My husband was doing research at the National Archives and the location was ideal. It is a short walk to the archives, Kew Gardens railway station and shops, Kew Retail Centre, the walkway along The Thames and Kew Gardens.
The train connection to central London is good- it takes about 30 minutes to the centre of London and trains run frequently.

The apartment is as it appears in the photos. It is well-equipped and freshly painted and had all we needed for a one-month stay. It was clean and quiet.

We did not meet Lawrence but his agent, Lorinka, was warm and welcoming and responded promptly and helpfully to any queries we had.
If staying long-term at the apartment it may be worth joining the Friends of Kew Gardens (62 pounds for two people/annum) which allows unlimited visits to the gardens and early entry. Single visits to Kew Gardens are 15 pounds/person. One can catch a bus directly to Hampton Court Palace (approx. 40 mins) from the road outside the apartment. There are boat trips to London and Richmond from Kew pier.