Workshop replacement..........

You can use any blocks you like, thermalite are perfect, although if it were me, I'd dry them out first or laying them will be a problem - they 'float' in the mortar if there isn't any suction, rather like sodden bricks and they'll take an age to stablilise enough to lay further courses, only lay 3 or 4 courses of thermalite (or other) blocks each day, leave to cure overnight and carry on - they become too wobbly otherwise, althogh it's rarely a problem, especially since you've got 18 linear metres of blocks to lay. Use piers and tie them into the exterior blockwork either with stainless steel ties or blocks. The footings may or may not be up to scratch, what do you mean by slightly sloping? Are the current underground blocks on concrete?

You'd be wise to shutter and concrete over the footings level, then build up off this...what's in the corner causing an obstruction? - the corners provide stability to the whole thing, so you may need to build more piers than you normally would.

HTH