YES! There were few occasion where my passport was not stamped when entering UK. I did keep record of entry and exit with my boarding Passes.
The burden of proof is on you so you may have to give an explanation when it was not stamped and you can get this record by approximate dates or when you started working. Many countries also stamp your passport on exit. Use those dates. You can also check your bank or Credit Card statements if you paid it by Credit Card
I kept a record on a small slip in my Passport so I have no problems. I suggest you start reading Home Office form so you know exactly what documentation you will need when you will apply for Naturalization.
Try to write a letter to the airlines also to see if they can give you a record of flying in and out. They usually keep record of it but they might not provide you for free, which they should.