The size of the company shouldnt matter as much.
You dont need to have offices in Bangalore, Rekyavik and Moscow to deliver an NHS IT solution. Realistically, there are dozens of UK companies that *could* have delivered this system but it seems that there is an institutional preference for BIG companies.
The private sector is just as bad though. Large organisations pay through the nose for services from (say) KPMG (even non-Audit ones) which can easily be done by smaller businesses, who are likely to be more flexible and keen to get the work, simply because there is the idea that a big company can "do more."
Frequently it is far from true, but I dont see how we can re-educate the globe.