The legal requirement for private flights is that lifejackets shall be carried for everyone on board when flying over water beyond gliding distance from land suitable for an emergency landing (Schedule 4 (2)(a) v) aa)). The terrain on both sides of the Straits is unsuitable for an emergency landing for some distance inland from the coast and you would be wise to confirm a suitable forced landing area on each side before assuming that you will be able to meet the requirements of Schedule 4. It would be easier, safer and infinitely more sensible to carry lifejackets.