Sorry to be the bearer of the bearer of bad news, but you're stuffed.
In the first instance, it was poor driving that led to this situation. You should've left enough time and been travelling at an appropriate speed that you could stop in time. Amber means slow down and prepare to stop, not nail it. That said, we've all been there and done it.
In the second instance, you have the word of two policemen against you, with zero footage to prove your innocence. In short, you're stuffed. It's more likely that the two officers were correct, as by your own admission you accelerated to get through the lights. I wouldn't even bother contesting it, you really are going to have to suck this one up and adjust your driving in the future. They cannot change the offence though if you challenge the FPN, so don't worry about that.
However, having a TS10 code on your licence will horrendously affect your insurance premium, as jumping red lights is clearly dangerous and could lead to them making a big pay out.