The police's response to your letter is likely to be a template letter which may or may not address any of the points raised in your undisclosed communication. Otherwise it is mostly meaningless/irrelevant beyond being an answer to any request to drop the matter as you are very, very sorry.
Generally speaking, whilst it is an offence to go through an amber light, unless it is not safe to stop, camera enforcement relies on 2 photos taken after the lights have turned red - proving that some part of your vehicle moved forward across the line while the red light was showing.
From what you have told us, they will not have such evidence. However, it seems more probable that the photos will show a slightly different version of events than you have told us. Also, whether the police would need the usual evidence in this case would seem to depend on what you did or not confess to in your letter.
Unfortunately, you are not entitled to see the evidence against you at this stage, and the usual ruse of requesting photos "to help to identify the driver" tends to be less effective when you have already returned the form naming the driver.
