I am a Corporate Insurance Broker and can definitely say that you need to have Public Liability Insurance. It is surprising that the Local Authority has allowed you onto their premises without it as they normally request to see copies of your insurance before hand so that they can not be held accountable.
As you are self employed (and presuming that the courses and workshops are run and organised by yourself, rather than another company) then you are ultimatley responsible for all matters while the classes take place. For example you need to ensure that the venue is safe and fit for purpose. With children involved you also need to ensure that all relevant checks have been done.
Your home Insurer will already provide an element of PL insurance but this will not cover you in relation to Business/Commercial activites - you need to approach a local commercial broker to obtain the cover although given that your opperation is quite small you should be looking at no more that �100 or so per annum.
Before speaking to your broker it would be wise to check with the local authority as to what limit of Indemnity they require of you - it is normal for this to be set at �5m of coveraged for all contractors who work on or in council/local authority buildings. Once you know the limit and requirements speak to your local commercial broker and they will be able to gain a quote within a hour or so for you.