Free Traffic Legal Advice

Hi there, just wanting a bit of advice how to proceed with a situation I have found myself in.

I passed a police officer on a roundabout by changing to the center lane and then returning to the outside lane to exit by the second exit, straight on. They were in a queue of traffic on the roundabout turning left which was only just starting to move. The roundabout has two lanes but only one lane for the exit. I believed they were turning left due to their positioning but they left via the same exit as me and pulled me over.

The officer alleged that I cut them up and did me for inconsiderate driving. I asked to see their dash camera as I was certain that I hadn't done so but was told there is no camera and that it would be my word against two police officers.

I luckily managed to obtained footage of the alleged offence from a shop's CCTV which shows that I started to change back into the outside lane a couple car lengths ahead of them when they were travelling at about walking pace - it is clear from the footage that no-one had to alter speed or direction because of me.

Upon recieving a course offer I asked for them to clarify the alligations and then challenged the inaccurate statement of the officer evidencing this with the footage. They have not yet replied to this but have withdrawn the course offer and issued a FPN (offence code RT88576).

I am quite stressed at the situation, I feel I have been treated unfairly and would be very grateful for some advice, particularly on the following:

1. Having a court hearing would be both inconvenient (I live about 2 hours away from the issuing authority) and intimidaing for me. Is there any way I could contest this without having one and if I do have one can I be reimbursed for costs?
2. I can't really afford legal representation but also probably don't qualify for free help. I feel the evidence for my case is strong so would representing myself likely be appropriate in this case?
3. The offence I have been accused of is for inconsiderate driving ("without reasonable consideration..."), is it true that to be found guilty they would need to prove that I caused someone to be inconveninced; would this mean that I would have had to cause someone to brake / change direction? (this is probably the most obvious thing to argue)

Best wishes,

S