I think that one of Birmingham's main problems is the mix of LCC passengers and mainline Economy passengers using the same terminal facilities. The two should be separated and be given facilities appropriate to their chosen "style" of travel.
I don't agree. Part of the reason why BHX merged both their former T1 and T2 (Eurohub) facilities together was to realize the benefits of a single passenger throughput. Not only can it make core operational processes more efficient, it allows every passenger to get the full "experience" thus maximizing consumer choice, and that's only getting more important as airports diversify their income.
People who fly LCCs are also not necessarily budget spenders and may actually be willing to spend extra in airport Terminals to upgrade their experience to something more premium. Putting those passengers into a basic Terminal with few facilities is ultimately lost revenue.
There has to be a solid business case to segment passengers in this way and I can assure you that, for probably any UK airport, there simply just isn't one and unlikely to be anytime soon. If you look around, you'll find there's actually little evidence to show low-cost terminals give any long-term competitive advantage to airports.