I began working in July and have had to pay my NHS insurance straight away
We don't pay an NHS fee. Do you mean the NICs people pay when they earn over £156(?) per week?
The NICs go towards a UK state pension, presently 10 tax years to qualify for the minimum state pension and 35 tax years for a full UK state pension. UK state pensions will only be paid out based your own NICs. Being in receipt of a UK state pension will mean that if you decide to retire to another EEA country, the UK will meet all your health bills in that country to save you having to buy health insurance to pay your bills. That being in receipt of a UK state pension will also mean that if you live in the EEA and would prefer to have treatment in the UK, you can pop back to the UK for free use of the NHS. That's the only connection NICs have to using the NHS.
Type 1 NICS payers can claim contribution based benefits, provided we paid them for the previous two relevant tax years.
The money for the NHS comes out of general taxation. Being able to use the full National Health Service for free has nothing to do with paying taxes or NICs to the UK. Even some born and bred Brits aren't allowed to use their own health service for free. Some immigrants who work and pay taxes in the UK are not allowed to use the NHS for free and nor will these people be allowed to buy this £200 a year Immigration Health Surcharge which also covers existing conditions. These people have to buy their own full health insurance to meet the NHS bills of themselves and their family.