What is the value of an Enfield 308 bolt action sniper rifle?

No such rifle. The Lee Enfield was made in caliber .303 British, not .308. The closest thing would be the Ishapore 2A or 2A1 rifle, made in caliber 7.62 NATO. While similar the .308 Winchester, it is not the same, and .308 should not be fired in a 7.62 NATO rifle.

The Lee Enfield "sniper" rifle in .303, if original and complete (and not an aftermarket conversion) may sell for around $1500, depending on condition and accesories. There are many fakes on the market- be sure of what you are buying.