Find a garage with an older (and therefore wiser) mechanic, or:-

Jack up the front off side and remove the road wheel. Also remove the nearside headlight for better access to the auxiliary belt. Support on axle stands. Send Siobhan under to unscrew the two (or is it three?) cross-headed screws holding the black plastic aux belt protective guard cover. You don't have to take the auxiliary belt off (though if you do it's quite simple to replace). Use a long 14mm ring spanner to swing the sprung tensioner wheel away from the belt, and holding it away, try twiddling the idler pulley. It shouldn't have any front-to-back movement at all. If it has, it'll squeal on start-up then go quiet as it gets hot and expands. If it's been left loose by the incompetents who have just ripped you off, then tighten it with a 16mm or 5/8" AF ring spanner. I know this because I didn't tighten mine up properly and twisted my knee when I had to get back under. The term 'incompetent' applies. Inspect the crankshaft pulley to see if there's any rubbery bits sticking out of the circle half-way out from the centre. It's a damper pulley with an inner and outer part bonded by rubber. They don't (usually) fail in a way which will cause your squeal. Twiddle the power steering pump's pulley and see if there's any play. Twiddle the tensioner pulley before letting it back onto the belt. Check all the grooved pulleys for any foreign substances. Ensure that the belt is correctly positioned on all grooved pulleys. Replace the black plastic guard and refit the air-con hose to it (held by three small tie-wraps if the car has air-con).

Incidentally, if the car does have air-con, then taking the alternator out of the engine bay is a nightmare and an expensive labour charge.... Without an air-con compressor, the alternator will drop down and out, but with a compressor in the way, you have to dismantly a power steering pipe (some mechanics take the pump off) and move lots of other bits, including bending the dip-stick pipe to one side, before the alternator can be lifted up and out. You also have to unscrew the battery-lead connector from the side of the alternator (just a nut and an insulated torque-head screw).

An unusual fault! But the 'professional' mechanics should have spotted that easily - and ripped you off for a brand new headlight which you could have got for half the price off e-Bay! And it's not stopping the car running, so there's no desperate need to fix it immediately..