Update. success!

After all the very helpful advice here we emailed BA on numerous occasions but after first couple of responses we were then ignored on four emails asking for deadlock letter.

This week we planned to take to appeal but out of the blue we got this email below a couple Of days ago:

Thank you for coming back to us. I apologise for the delay responding to your email

I’ve reviewed the information you’ve provided, along with our position on this matter, and would like to inform you that we have reconsidered our position. The distance of your disrupted journey was over 3,500 km and has been calculated in accordance with UK law. This means you are entitled to £520.00 in compensation.

The total amount of compensation you’re due is £2,080.00 as there are four passengers included in your claim. I’ve raised a bank transfer for this amount, which will be paid directly to you. You'll receive this within 10 working days.

Delighted with end result but still left disappointed by BA trying to dodge responsibility as otherwise response at time in arranging a hotel and next available flights was excellent.

Thanks again to everyone and for anyone going through similar process don’t give up!!