Most of clothing sold in the UK is sourced in China, Bangladesh, India, Turkey and Romania. Each country has different issues. Egregious child labour is not such a problem in China as in India and Bangladesh (particularly in labour intensive hand finished garments with sequins etc...) . In China the issue is health and safety, and overtime above legal limits (although the legal limits are considered unreasonably low both by employers and employees so they both flaut them). child labour is also a big issue in the cotton supply chain.
Point is low price doesn't necessarily mean child labour, and child labour isn't the only ethical issue in the clothing industry - there is the right to join a trade union, working hours, health and safety risks, bullying at work etc.,,
The thing about Nike and Gsp in the 1990s is not that they were actively seeking out to have their clothes made in bad conditions, but that they didn't know, and didn't make it their business to know (very few clothing companies run their own factories and there is a lot of sun contracting)
For my money Nike and Gap have been the leaders on supply chain labour standards, H&M and Zara the it seriously. The cheaper stores Asda/Walmart and Primark have dragged their heels more because of price pressure but are getting the medsagr. It s always good to tell companies you care about this stuff - write to them, ask shop floor staff about codes of conduct for factories etc..
Primark's cheapness is more down to low quality, high volume sales - which has negative environmental impacts - rather than uniquely poor labour standards.
Most child labour is on farms, in domestic industries and in the informal sector and as servants not in export manufacturing.