If you were studying only then would have needed comprehensive sickness insurance. But because you were working as well, you can claim to exercise treaty rights as a worker. As the other member have pointed out, you can try to extract as much information from your previous employers, and then also contact HMRC and ask for your tax/ni records/statements for past years.
Once you have this, I would suggest you do not apply for naturlisation. You should instead apply for confirmation of Permanent Residence. The benefit of applying EEA4 is, that the fees is only £55 and if you are refused you only loose £55. But if naturalisation is refused, you will loose most of £864.
Now, one more important bit. If you apply eea4 and supply them with your initial 5 years proofs documents to prove treaty rights, and that application is granted, then you will know you naturlisation will be granted. But if you apply eea4 with last 5 years proof, then you will have to wait one more years to apply for naturalisation. Still not a big deal though.
regards