Hi Malcolm,
The idea, apparently (Mr. Haynes) is that you press the stainless blade in and use the key as a type of puller...great when they have been in and out a few times and lubricated, but not when out for the first time (in ages) and are gummed up with crud, old hard grease and a bit of corrosion.
I usually have success as follows..douse the offending barrel/latch assembly in Plusgas before trying anything, insert the thin bladed screwdriver into the slot where the stainless blade lives and push it in towards the barrel body. While holding this screwdriver in place, carefully insert a wider thin bladed screwdriver under the plastic shroud that covers the outer end of the barrel and slowly/carefully prise/lift the barrel out.
I have had to do this several times with various barrel/latch assemblies and dismantling the latch body assembly as a whole (due to failed return springs - see post on springs from RS) and could probably do it with my eyes shut now...
HTH
Glyn