The advice you have received from HMRC is correct. If i understand correctly, you leave early to change employer and the bond falls due. The bond liability is therefore yours and so any routing of the payment will still discharge your peculiarly liability. If this happens "by reason of (your) employment" then this is taxable income on your part. The UK employer is required to include the value in your taxable income and account for PAYE.
There would be no UK tax if the payment was not received - from your viewpoint - by reason of your employment. For example, suppose they paid your bond for the privilege of meeting you for interview, with no guarantee they would offer, or that you would accept, employment. Very difficult to believe they would do that (and that would most likely be the view of HMRC if it actually happened!).
Sorry
If you think the potential new employer wold pay your bond, you could hope that they will also pay the tax (the gross-up calculation will apply) or you could offer to pay the tax (the gross-up calculation is avoided, but you get to pay the tax).