I had the same problem last Wednesday. Tried calling and the website at the same time but no luck. Was travelling during the day and tried again in the evening, again with error messages on the website and a continuous engaged tone on the phone.
Eventually managed to book my Plymouth-Santander-Portsmouth trip plus Commodore cabins with an optimistic sigh of relief at 1040pm on Wednesday.
Happy days…until a phone call taken on Friday at lunchtime from BF. "Mr Knocker I'm afraid your booking for the Plymouth-Santander sector and Commodore cabin was duplicated due to the excessive website demand." Conversation, not repeatable on this forum, resulted in us having to move our outward departure from Portsmouth to Santander losing three days of holiday. This was all going to be made acceptable by meal vouchers for us to use as an apology from BF.
I questioned at some length why BF go through this process each year knowing that their website and phones are going to be bombarded with hits and calls. Was told that despite an increase in telephone operatives there was nothing more that could be done. I suggested them staggering the launch of summer bookings over a period of days ie France followed by Spain to ease the pressure. "Well thats a very good idea sir which I'll pass on to our planning team for consideration".
After the end of the call I wondered why I had not simply said "no way, my booking must stand due to (wedding etc etc)" and let the other poor soul fight out an alternative. Wondered then if there were 4-5 people all expecting to share the same cabin booking! Too soft I guess but this problem is not going to change unless some practical changes are made to website ability to cope with significant pressure, telephone system improved ("you are currently 1,300 in the queue but we take your call seriously and our next operative will be ready on Thursday morning…) and the practical option of releasing sailing bookings on staggered basis.