I am suggesting that UK border police do not maintain control of British beaches, and do not examine the passports of people getting into boats, and do not arrest them
Under what British law can British border police arrest people getting into a boat?
Border force are a multi agency and have powers as both customs officers and immigration officers. They also have broad powers under counter terrorism legislation. I have been contacted by UK BF and other states equivalent several times. I've been boarded a few times in the Med. They are mostly concerned with the coding of equipment and chance to check papers.
For BF If they suspect a person is not a British citizen they have very broad powers - stop, search, test, detain etc. Once they are satisfied you are a British Citizen with the right to be in the UK, the immigration officer powers become very limited, unless they think you are trafficking or facilitating. They can also search for any relevant documents which establish the person’s immigration status and ID, meaning the person’s belongings – including electronic devices - could be searched or seized.
Paragraph 2 (1) and (3) of Schedule 2 of the Immigration Act 1971
Section 26 (1) (b) of the Immigration Act 1971 and Paragraph 15A (7) of Schedule 2
Police and Crime Act: Maritime Enforcement Powers
The Merchant Shipping (Safety of Navigation) Regulations 2002 (SI 2002/1473) - some parts apply to pleasure vessels.
It's worth remembering that these craft would be classed as "Passenger Ships" irrelevant of their construction as they are intending to carry 12 or more people. So there is no argument that it's just a dingy on a beach. If you did this as an experiment in the Solent for example, you'd get stopped within about 15 minutes.