Without spending £x on either buying a machine polisher yourself or leaving it with a Detailer for a few days to remove all the paint defects your best bet would be to use a filler heavy polish like Autoglyms Super Resin mentioned above. This offers no durability on its own and needs to be topped with a sealant or wax to lock in the filling effect of the Super Resin.
Autoglyms Extra Gloss protection is designed to sit over Super Resin or a wax like Britemax Vantage or Autoglyms HD wax.
Happy cleaning!
Chris