"Fairly good" for £100. No chance. To give you a idea of what they can cost, my lad's "quite good" one set him back around £1200 - but he's 17 and rides competitively.
But for a seven year old girl, you may find something good enough for her that isn't total junk from £150. It will be heavy for that price, and the brakes, BB and hubs will be poor.
Does it have to be a BMX though? You really don't get a very good bike unless you spend a lot of money and even then you miss out on gears, decent brakes, a comfortable saddle, a light frame, wheels that stay true - the list goes on and on.
One piece of advice though - don't buy a bike from a big warehouse sports shop e.g. SportsdDirect, JJB sports etc. Their Dunlop / Reebok / own brand name bikes really are utterly and totally terrible.
Halfords worst are far better than anything sold in these places.
The best thing she could do is to buy a second hand Islabike, use it until your neice outgrows it, then sell it for about what she paid for it in the first place.