For Edinburgh, and Glasglow, try Albaladies, they would be better able to offer advice on this area.
Try this site. http://www.premierapartmentsbirmingham.com/
http://www.premierapartmentsmanchester.com/
I have used these in Ireland, they have them in Dublin and in Galway, and they generally don't have a 24 hour concierge, but what I do is I will call and put on the thickest American accent I can and act all paranoid and ask loads of security questions. Which works great, cause they want the business, and will tell you the most interesting details about how their security works and what not.