A car insurance company web page states I have to be able to say "yes" to the following in order to get a quote.

"I don't have any criminal convictions (non-motoring) or any pending convictions, excluding convictions spent under the Rehabilitation of Offenders Act 1974"

I am not sure if this applies to me or not.I have a criminal record but i have not been in trouble in over 2 years so does this apply to me or can i say yes?

How can you NOT be sure...? Either your offences are spent or they aren't.

Consulting the exact car insurance company would be a better choice, in my opinion. Because those rules can change depending on the company. And you should keep this in your mind.

You should go up with this car insurance company. It is not at all being affected by your criminal record.

It does apply to you and always will. If you have an Enhanced CRB check that conviction will show until you are a 100 years old. if you write no and have an accident, they will find out through the PNC and your Insurance will be invalid.
UK

The company fills in the computer blanks and then the computer computes a quote.

That is the way it is.

Depends how old you are and what the sentence was, but I'd say you have to wait at least 2.5 years.

For adults, the rehabilitation period is 5 years for most non-custodial sentences, 7 years for prison sentences of up to 6 months, and 10 years for prison sentences of between 6 months and 2½ years. Prison sentences of more than 2½ years can never be spent.

For a young offender (under 18) the rehabilitation period is generally half that for adults.