A good place to start is to look at the LB of Lewisham, a large number of street & park tree locations were imported into OSM back in 2010. Whereas some of this data is probably outdated, particularly around redeveloped estates, it gives a reasonable impression of what one might aim at.
Like you my experience with the London Data Store tree dataset is that it needs to be checked on the ground.
I have a partially cleaned up version of the LDS tree data, which provides accurate values for species or taxon where possible.
A reasonable strategy is to use the LDS data as a starting point, but quickly cross-check it. Cross-chedking can be simple “is there a tree in this location?” or complex “is the tree shown in this location the actual species and cultivar shown in the data?” The former is much much quicker, but the latter is likely to uncover errors in encoding in at least 2-3% of cases (based on my own sampled surveys against tree open data in various locations).
In general a council provided data set is likely to provide more geographical accuracy than trying ot survey locations yourself. I find GPS surveyed data compared with data from a council GI usually highlights the inadequacy of the using just a GPS.
Long runs of street trees, typically London Plane or Common Lime, can be resolved fairy quickly. Combining checkig that trees are still there with other surveys is likely to be highly useful.
Hi Jerry/SK53 thanks for this. I am not sure whether his forum allows to send personal messages so asking this way. Would you be willing to share with me a copy of the cleaned up London tree database? Am planning to spend some time on this at a a weekend soon. Best wishes Ellie