In reply to Tigger:
Ignoring the possible £20k fine... To attempt kill a mature tree close to property/people is dangerous. You do not know when the tree will die, when the storm will come, when it will fall or shed branches or potentially mame or kill someone. Mature trees are hard to kill precisely, most suggestions above are at best ill-informed nonsense and unlikely to work but will weaken the tree and cause more problems. Depending on the ground conditions tree removal close to property can be ill-advised too, as changes in the take up of water around a tree can cause heave or subsidence in buildings.
Given your application has been refused it may be best to submit a planning application for tree works to crown lift or remove selective branches, deadwood and de-cone. The works and application is best done by an Arborist if you are not familiar with tree works, BS3998 or TPOs. Pruning can make a significant difference. If you prune and the situation does not improve for you, it puts you in a better light for subsequent applications to remove. An arborist is likely to charge approx £350-£450/day if climbing the tree and a groundsman required (relatively small tree should take 1/2 day).
It is possible to get a TPO removed (I have done) but you need a compelling, real and concise argument. I believe best to focus on one or two key issues rather than a shopping list of woes. You need to engage with the local tree officer first and it may help to discuss 'process' with local Councillors on the planning committee. If there is a compelling argument a council will generally be reasonable, you can seek appeal if otherwise.
ps - this tree sounds relatively small for a Scots Pine at 40'. Alternative native species may give you other problems - so be careful what you propose as a replacement (much research needed).