You can ask for a backdated claim but it may not be payable without good cause for the delay. If you were available for work and what is called actively seeking employment (ASE) during that period, NI credits can be awarded so you need not pay for them. ASE includes such things as looking in the papers for jobs, searching on the internet, asking friends and family, going to the Jobcentre, 'phoning or writing to employers for example. If you can show you were doing a few of those steps each week, you should be classed as ASE.