I'm going to answer this in a few chunks, probbaly most people will find this boring but I have done the research so I may as well share it here.
SCOTLAND V ENGLAND
The offence in England is in the current Regulations, here abridged to
"no person shall cut down .... any tree to which [a TPO] relates, or shall cause or permit the [cutting down of] such a tree, except with the written consent of the authority"
In Scotland it's in the primary legislation and the equivalent is -
"If any person, in contravention of a [TPO] cuts down a tree, ... he shall be guilty of an offence."
As I will explain below, I don't think that this means in Scotland that you are off the hook if you get someone else to cut your tree down.
THE POOLE CASE
I have only seen the appeal judgement. The appeal related only to the person who told the tree surgeon to do it. The appeal related only to the applicability of the Proceeds of Crime legislation. The original decision was in Bournemouth Crown Court. I have not seen that judgement. Mr Davey's fine was £150k, including value added to his house by improved views.
In the case, it is at least clear that the tree was not even on Mr Davey's land, and he knew it. He got his neighbour's TPO'd tree cut down. There is nothing in the judgement to say that the tree surgeon's relatively paltry fine of £2k was for breach of TPO. It could have been for proceeds of crimes including criminal damage and trespass.
So, I don't think this judgement in itself is proof of the ability of COuncils to fine contractors. Even if the Crown Court had done that, it was not appealed and could have been a flawed decision.
MAGISTRATES COURTS ACT
I suppose smaller prosecutions than the Poole case are handled by the MAgistrates Courts. Section 44 of the Magistrates' Court Act 1980 provides that any person who 'aids, abets, counsels or procures the commission by another person of a summary offence' is guilty of the like offence. That seems to open the way for contractors to be fined too.
THE CONTRACTOR'S POSITION GENERALLY
However, aiding or abetting is only punishable when the aider or abetter knows that it is a crime he is aiding or abetting. If a contractor innocently helps bring about a crime or asks if the customer has checked for restrictions and is told yes, it is nothing short of ridiculous for the law to prosecute him. What benefit would arise? Well, the only one I could think of would be scaring the industry into becoming tree police for the Council. That is clearly clearly not the law's intention.
The English Act is more explicit about whether a tree is merely cut down or is caused ot permittedto be. But fundamentally this cannot change the basic point. Trees don't move. They go with the land and so the resonsibility for them and for adhering to laws relating to them (like Occupiers Liability Act) rests with the occupier (usually but not always the owner).
The offence of cutting down applies to when an occupier does it himself, and to close a potential loophole you can't wriggle out of it because you got someone else to do it, or turned a blind eye while it was done. In Scotland we don't even see it as a loophole and don't have to spell it out, that is why our wording is simpler.
If a contractor cuts the tree down and has been appointed to do so by the customer, the customer is very very obviously causing the the to be cut down. Unless the contractor knowingly aids or abets this (i.e. knows it is wrong but does it anyway), he is blameless.
THIS AND SIMILAR CASES
I think the OP is blameless. If a prosecution went ahead, it would be his word againstthe customer's. And if a court couldn't decide who was tellign the truth, the default position in my mind is that the occuier is guilty. If the ofccupier disagrees with the judgement, he can sue the contractor on the balance of probabilites principle.
Me? I'd say nothing to nobody. I checked, the occupier said he knew of the TPO and that it was OK. Note in my diary to that effect. Invoice and payment on file. QED. If prosecuted or offered a caution I'd fight it till I was penniless, and then I'd keep on fighting. Who'd want to accept living in such an unfair society if something could be done about it to set the record straight for every Council in the land. Councils get these things wrong, all too frequently. Well, England anyway. Till I move there, which is not anytime soon, I am satisfied that my view on how the law would be interpreted if push came to shove is about right.