i live just outside Southampton so bit far to travel to look really, although it's not out of the question if we could come to an arrangement on my travel costs.
i have been in the game over 20yrs so know a little bit : )
pretty sure you will get a cheaper quote but i'd advise strongly that you see the insurance of whom ever you use, not to rush in and use the cheapest guy as cheap isn't always best .
from what you have described already this sounds like it's not a straight forward job, also the tree may be unstable and in an unsafe state.
and finally please make sure that you have the relevant approval from your local council tree preservation inspector otherwise you will find you may be liable to a rather nasty fine even though from what you have said the tree clearly needs attention .
i'm sure that once you have had half a dozen or so quotes you will be a lot wiser after all the free advice. GL : )
The vegetation report mentioned some fungal disease and the guy today alluded to the fact the roots could be diseased and he certainly saw it as unsafe. If it's not already unsafe it's heading there quickly as the ground is quite disturbed and the tree has listed to one side.
I would really value some advice from someone I 'know'. If you PM'd me what you think would be your travel costs I'd almost certainly go for it, especilly if you could come tomorrow !