A mountain bike running podgy tyres at a relatively low pressure might be more comfortable than your Raleigh.
A cheaper approach would be to try to improve the comfort of what you have.
A suspension seat post is worth a try, as is running the tyres at a lower pressure.
I'm no fan of suspension forks, but you could try to establish if yours is set up correctly, although there might not be a lot in the way of adjustment.
Podgier tyres would give you roughly the same comfort improvement as a mountain bike.
They would fit on your rims, but may not clear the frame or mudguards.