Agree with Wannabe, this is exactly right. More often than not, the beadwork/ handwork is done by "outworkers" usually women and since the majority of these women have young children they are not able to work in a factory under factory conditions so the work is sent to the house. There are not many factories I know of in India that do beading on site unless it is machine embroidery/ beading which is quite rare (and considered less desirable by consumers).
I have visited textile factories in both India and China but obviously when I go, there are no children around and there are plenty of signs up saying "we don't employ children under the age of 16" but this is not to say that these factories do not use outworkers.
Another point, Primark uses factories that Gap, French Connection, Toast and other more expensive brands use so they are not necessarily using factories who make cheap clothing and therefore have unethical standards, they are just bigger players, buy bigger, have less overheads and have lower margins.
As others have said, as sad as it is we cannot impose our western ideals on to these countries, i suppose the first step could be regulation, so children are allowed to work but have to spend a certain numbers of hours at school/ in play but I don't know how easy this would be. What we have to remember is that it is not necessarily corrupt factory managers or owners who are pushing the children to work, rather the families who will get paid for buy the qty of work done and so will get all hands on deck to earn more money than the family.