The response of airlines to the storms of this winter was utterly inadequate, both in the UK and the US, when the storms hit the east coast. The airlines have shut down their customer services and sought to shift booking towards the internet. This is fine for routine situations, but is utterly inadquate when there is a crisis. This leads to people being stranded and left utterly helpless.
BA claim that they had developed a system which allowed people to rebook via the internet. It didn't work when the demand was so huge. They need systems which allow for exceptional demand in a crisis and they don't have them. There are similar complaints all over the web when the storms hit the east coast and airlines left passengers stranded for days.
In your case, you are entitled to compensation. US based airlines have a "get out of jail free" card, of being able to blame the weather. All consequential damages are not then their responsibility. However, as you booked on an EU based airline which travelled via Europe, you have some remedy via EU261/2004. This does not allow the airline to escape it's obligations entirely and blame the weather.
However, a note of caution. Your have a legitimate complaint that BA failed to properly rebook your tickets to Cairo and this resulted in losses for you. You may not be able to make the case that the airline would have been able to rebook you the following day if they were not so incompetent. In fact, this storm came at one of the busiest times of the year and so many airlines were fully booked. The scale of the disruption was such that the chances of availability on other routes was slim. Do you realise that CDG and FRA and AMS also closed during this storm and as a result there were literally hundreds of thousands of passengers stranded. Availability was severely limited. I do not think you will receive the lost booking fee's... these are more likely to be covered by your travel insurance. I assume you had some, as it would be bonkers to travel to Eygpt without insurance!
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