Hi Sarah. As Top-Consultant mostly helps consulting firms to recruit experienced hires rather than fresh graduates, our interactions with recruiters don't tend to shed so much light on what's happening with the graduate intake. So I'm afraid I can't shed light on which specific firms might be delaying start dates in this way.
However I thought you'd appreciate the crumb of comfort of knowing that this is not at all unusual when the market takes a turn for the worse. The most recent round of milkround recruiting will have taken place when the firms were collectively projecting another year of buoyant business - and obviously with the recent economic developments this is no longer the reality.
There is really nothing worse than being a new hire in a consulting firm and finding yourself "sat on the bench" / "on the beach" for months on end - ie. not out working on a paid client assignment. It's demotivating, you're not learning anything and as your unproductive cost to the firm rises so does your risk of being made redundant, which is a far more serious outcome for your career than having your start date delayed.
For all concerned it's therefore much better to have a delayed start date so that the firm's headcount is brought more back into line with the revised level of client demand.
Your situation - whilst not ideal - is far better than those who'll be graduating a year later and will find the milkround hiring opportunities significantly scaled back as firms are still trying to accommodate those made offers in your round of milkround recruiting.
My best advice would be to mentally prepare yourself for something fun / rewarding / challenging you'd like to do if you do find your start date put back - ski season, living abroad to learn another language, etc.
Hope this helps and all the best