I have been offered a limited number of sessions, but I realise I need many more

A lot of therapy approaches are intended to work only for a fixed number of sessions, because they are based on a clear progression of steps that will take a predictable amount of time. Other approaches run much less to a pattern, and may work best over a long (perhaps a very long) period. But when therapy has been obtained free of charge through the NHS or through the voluntary-sector, it is usual to have a limit placed on the time available because of the pressure of waiting lists. If your model of therapy works according to a fixed number of sessions, this is not a problem. But when the type of therapy used would normally be more open-ended, you may feel that the sessions on offer come to an end just when the process is proving to be useful.
Sometimes it is best to see a limited number of sessions as a preparation for longer work, and a way for you to discover whether therapy helps you, or at least whether this type of therapy helps. On other occasions the limitation may even focus you more determinedly on the difficulties that you are experiencing so that you make sure that your efforts are directed towards the right ends. It is not always helpful to view counselling as always being about 'resolving' long-term problems over many years. Therapy may last a long time, or it may be very brief indeed, depending on what you intend to achieve.
If counseling sessions are due to end at a time that feels “too soon”, discuss this with your counsellor. Occasionally the period of support can be extended, or perhaps there are available alternatives that can be recommended. Having longer therapy is always a possibility, but it helps to think through whether it is needed and what your expectations of continuing with it would be.