The Raleigh Pursuit is a mid level bottom of the ranks for Raleigh, it never had a derailleur hanger.
This is an easy conversion to Single speed and would be a fun bike.
First thing, remove the freewheel from the hub then

Center the axle in the hub
1, remove the outer locknuts from both sides of the axle
2, loosen the cones from both sides and remove the bearings
3, clean and inspect bearings and races and replace while centering the axle in the hub.
4. replace the spacers making sure they are the same on both sides.
5. snug up the bearing cone lock nuts making sure the wheel spins smoothly.

Recenter the wheel
1. Put the wheel with the centered axle in the bike and snug the wheel nuts or QR skewers.
2. use the brakes as a gauge to center the rim in the frame by loosening the spoke nipples on the side closest to the frame and tighten the spoke nipples

install a single speed freewheel.
Buy a cheap single speed crankset and install it
put on a chain and ride.