HCEO vs County Court bailiffs -advice needed

Possession - Section 8 and Section 21

We have just been granted a possession order under Sec 21 after court hearing.  It's been a stressful journey to get to this point (long history of access issues for repairs, complete loss of trust in the tenant and financial impact due to making a loss on rent vs costs) and we ended up with court hearing as tenant lied on defence form about not receiving Gas safety certificates/ How to Rent guide/ EPC etc.

We're keen to move forward with enforcing the order as soon as possible.  The property is in a London borough which is known to have long county court bailiff wait times.

We know we may lose money if we apply for transfer to High Court for use of High Court Enforcement Officers but the application is turned down.  Is anyone aware of any other reason not to apply?  Could applying affect our possession order in any way?  I don't think so  but would be good to know if others have experience of this.  Thanks!