Hi, having previously worked as a consultant with a different firm, also specialising in third and public sector work, I would agree with the above post. This is a reasonably realistic expectation. The big difference for me, when compared to my current organisation, is scale. I had nowhere to go before because the next layer was director (all reasonably young and not looking to move any time soon) and a natural cap on any salary increases as the organisational ethos was to maintain senior management salaries as a sensible multiple to the lowest paid member of staff. This model, albeit admirable, meant my salary was squeezed into the last available segement before director. In a larger organisation, there is more scope to specialise and to negotiate salary increases.
Also, as an aside, on many projects I worked on the availability of funding - secured by the client - could often dictate the volume of support they could bring in from us and therefore dictate the scope of our involvement in the project. In some cases helping the client to achieve buy in from external stakeholders was one of the enjoyable but time consuming elements and when time was squeezed due to funding this would usually be the top unavoidable drain on time.
I hope this helps and doesn't put you off. I loved the experience but found it didn't offer enough for me personally to stay on a long term basis.