Chris at eden

I think you have a bigger problem here than you realise and i am not being some kind of a tree hugger.  Just to clear up the timing.  If you damaged the tree before the TPO was made then there is no criminal act.  If the damage was done after then you will be lucky to get out of this without a criminal record.  Someone mention a £20k fine but this is incorrect, the max fine for willful destruction is now unlimited even on summary conviction (i.e. determined by a magistrate).  Then you have the potential to be hit with proceeds of crime, court costs, and replacement planting.  I also wouldn't be entirely comfortable with the only person that can prove that you did the damage before the order was made is the tree officer, the bloke who is going to try to prosecute you potentially.  If it was me, i would have taken a photo myself and emailed it to myself so it is date and time stamped.      
 
As to why the council can come onto your land and make a TPO.  They can do this as there is a piece of statutory legislation that has been in place since 1947 that allows it.  They have a right of access and if you try to prevent them it is a £1k fine. This is just a fact, the analogy you use about interfering with your neighbours land isn't relevant.  If you want to build a big extension on your house you will need planning consent.  Its the same legislation. 
 
But assuming the damage was done first.  
  
I don't see why the tree officer would have TPOd the tree just to let you fell it.  If it isn't dead, and there isn't an immediate risk then the works are not exempt so you will need to submit an app.  As the app is based on condition it will need a tree report and i dont see them accepting one from the tree surgeon you mentioned just saying fell.  If you send that in then they will just refuse it saying there is no consideration of the options.  You will then go to appeal via the planning inspectorate (PINS).  The LPA can take 8 weeks to determine the app.  You then have 28 days to appeal and get the appeal registered.  This takes you up to 3 months.  The PINS deadline is 27 weeks which will take you up to 9 months best case scenario.  The PINS are nowhere near meeting their deadlines, i have just had one back that took 11 months just for the appeal, 14 months in total.  Not good.  Then, you may not win.  If the TO says you could look at other options such as bridge grafting then the inspector may agree. 
 
The TO will most likely have a degree in Arboriculture and the PINS inspector will rely on this in part as they wont be a tree expert.  They will look at the expert evidence supplied by the TO and you.  As such you would be better getting your report from a consultant.  Problem you will have is that the consultant should really look at all the options which will include trying to save the tree.  The TO could then say why not go for this option.  
 
As i said i am not trying to be a tree hugger here, I'm just giving you the facts.  As a consultant i wouldn't take this on either.  I am not going to get into the whole debate as to whether what you have done is wrong or not.  But, tree consultants have to work with tree officers all the time and so its good to have a good working relationship with them.  If they are going to be picky with all of your future reports that you submit for planning because of a one off £500 report, its not worth the hassle. 
 
The fact that the neighbours don't like the tree is not even remotely relevant.  TPOs are always made when trees are under threat and so against the wishes of the owner and neighbouring properties.  Again just a fact worth sharing.  I have heard loads of people say they put the TPO on the tree without my permission.  That is how it works.
 
Replacement planting.  If the tree had died and become dangerous they would probably accept a standard as a replacement.  £400-ish.  They will almost certainly push for something bigger in this instance.  Think thousands, not hundreds.  
 
As i said, not a simple or quick as you may think.  The TO can easily delay the felling of the tree for well over a year.  They dont even need to confirm it for 6 months and you cant register an appeal until the TPO has been confirmed.  You are now up to 20 months.  Not saying this will happen but there is no reason why it couldn't.  This gives plenty of time to see how the tree responds.    
 
You need to get some proper advice on this realistically.  You cant get a proper assessment by posting a pic on here.  If it falls and injures someone in the meantime you will be liable.  Irrespective of the TPO.  The only way you can shift any liability toward the council is with an application supported by an expert report.  
 
Note.  i have not visited the site or inspected the tree and so the above comments are for information only.  They must not be considered as professional advice under any circumstances.