I am not really legal expert and would really appreciate if someone can provide me legal advice on below case.
I missed my BA flight on returned journey to London and here is my perticulars of claim and situation how it happened;
Time of online flight check in: 8.55 pm GMT (flight departure next day morning time 7.40 am GMT).
Time I arrived at the check in desk to drop off my luggage: 6.25 am GMT but there was no one available at the check in desk to collect my luggage.
Official time of baggage drop off deadline: 6.40 am GMT
I waited for 5 to 10 mins for someone to turn up but no one came so I rushed to the airport help desk from there help desk helped me to connect with BA supervisor at CST Mumbai Airport.
Time of call to BA supervisor: approx. 6.45 am GMT.
BA supervisor advised to call reservation desk to change my flight as he was unable to help and also told me that he don’t have anyone to re-open the check in desk for me.
Following above advice, I called reservation desk and request for flight change. Time of call to BA reservation team in Delhi: 7.00 am GMT.
Reservation girl informed me that there is only 1 flexible ticket available @£697. I explained her whole situation why I am going to miss my flight and asked why I should pay when it was BA’s fault? She went away to speak with the supervisor and then offered to waive the cost of the ticket but said I will still need to pay the government tax @£113 for the alternative flight ticket. I had no options left as I wanted to return to London asap due to work. So I asked her to book the next available flight which was 12 hrs later after the departure of my original flight. During the call with reservation girl I made a note of her name and her employee number, telephone number and the time of call on a sticky note (I still have this with me).
When I boarded the plane, I noticed there were many seats empty which made me wonder why BA sold me only flexible ticket when they clearly had many seat left? Additionally, when I returned to London, I noticed from my bank statement that BA charged me full ticket price @£697. Furiously I wrote to BA about the full ticket cost they charged me when their staff actually promised to waive the ticket price but ask to pay government taxes and why I was sold only flexible ticket? BA responded with one line sentence that the amount charged on my ticket is correct. No further explanation was given. So I wrote them 3/4 times chasing for the answers but I didn’t received any response. Frustratingly, I wrote to the Retail Ombudsman who wrote to BA but BA refused to work with them. The Retail Ombudsman advised me to seek alternative dispute resolution method. So I made a small claim in the court.
Following the small claim in the court, BA has now submitted their defense to the court with denying all my claims and saying I arrived after the flight departure, i.e. after 7.40 am GMT, hence I was considered as no show however I was given a goodwill gesture and offered reduced flight ticket which was originally @£947. This was never mentioned to me previously and I learned about the original cost only from BA's defense. They are also rejecting my claim that there was no one available at the check in desk. As per their defense BA is saying the last baggage drop off was at 6.34 am GMT.

Now the court has asked me to fill out Directions Questionnaire N180 and EX730 form.
I am not really worried about the ticket cost but for me this is about the principles. I know for 100% sure that I arrived at the check in desk within time before the baggage drop off closing time. How can BA lie about this in the court?

Could anyone please advise me how should I go about my claim from here? Do I need respond to BA’s defence with my counter argument?
There are many travellers who miss their flight but BA don’t offer everyone gesture of goodwill so why they offered me? One must think that BA had realise that they are at fault hence they offered me gesture of goodwill but then they charged me full ticket cost; so how this work? And what happen to the promise made by their reservation team? This is clearly sharp practice by BA and praying on customers who are in urgent need.
BA must have recording of my telephone call with BA supervisor and Reservation desk. How do I ask them to provide this to me/court?
Also, there must be CCTV footage to confirm my time of arrival at the check in desk. How can I ask for the copy of CCTV footage for that day and particular time?
Under what law I can ask BA to provide telephone and CCTV recording to the court as an evidence?
I would very much appreciate your help and advice on above, please!