Hopefully your quote will have provided you with a SAP derived prediction of annual system output. This should have accounted for the shading in such general, overly-cautious terms that I would be very surprised if performance was hammered to the extent the SAP rating predicts (assuming it was indeed accounted for. If not, choose another supplier).
Modelling ‘soft’ shading issues such as that from trees, where a variable amount of light can pass through is very difficult. However, from real world experience I have been quite surprised how little the effects of shading actually do impact on system performance. For example, I tested an 18 panel system recently, split into two strings of 9 panels. One string had 4 panels heavily shaded by a chimney. It was a bright sunny day when I carried out the tests and the shading was obvious. However, both strings (the other being completely unshaded) were performing identically. Surprised me.
Also bear that there is plenty of diffuse light falling on panels most of the time (especially in the UK default weather setting of ‘overcast’), so even if the sun is hidden behind a tree, light will still be reaching the system and performance may not be affected too much.
Sorry, I’m waffling. No easy answer. However, it is important that your chosen system supplier has recognized and accounted for the shading issues. If not, find someone else.