The major problem with using QQ for independent certification work isn't really the degree of expertise or independence, rather unsurprisingly they are pretty good at being beyond reproach in that area.
The problem comes when QQ need access to overseas provided data, particularly data from the US. I needed QQ to provide assurance advice on some FADEC software. Technically they could do this, but the US refused to allow the code to be passed to a UK defence company; they would only allow the release of the code to a government agency. The solution was to use the CAA and FAA to undertake a military approval, far from ideal as it was outside their comfort zone.
My personal view is that T&E should never have been privatised, primarily because of the additional cost to the taxpayer that has arisen as a result.
VP