Hi.
It is hard to say if they will prosecute or not - it really depends on how their prosecutor views your actions. It is probably too early to get a solicitor involved, I would wait until they respond to your letter.
As to the content of the letter: yes, apologise. Don't bother mentioning your immigration status as it doesn't excuse your actions. Don't mention a specific amount as it can be seen as trying to 'bribe' them - just offer to repay the difference in price of the two travel cards plus appropriate costs.
I understand why you don't want to post in the general forum, but members such as DaveNewcastle have a lot more experience in these matters than I do.