When I stop pedaling my bike the rear gears keep turning, is this an easy fix? Bike is a vintage Raleigh Grand Prix Raleigh Grand Prix chain and rear hub keep turning when coasting
When you stop pedaling the freewheel on the back wheel is supposed to spin so that the wheels can keep turning but the chain, and the pedals are stationary.

Something is preventing the freewheel from doing it's job.
First guess is that it needs lubrication.

Repair Options:


Pull the rear wheel off and try working a little oil into the freewheel. This involves turning the freewheel backwards while applying oil in the gap between the moving part of the freewheel and the stationary part.
Disassemble the freewheel and lubricate
Replace the freewheel. This will require a special tool, your local bike shop should be able to help you. If it's off the bike some will remove the freewheel for free - others will charge.


Part number 42 in this diagram from Sheldon Brown's website  



Here is an list of the previous answers to this question (not a complete list). These articles contain information on what lubrication to use and detailed instructions for lubricating a freewheel.
"How should I lubricate my Shimano freewheel?
"What should I use to lubricate a freehub?"
Bike pedals turning when coasting (not a fixed gear)  

By the way, Sheldon has an article on the Raleigh Grand Prix 1968 to 1977 and a Raleigh catalogue archive