The law relating to your question is not written down in one single line of text, neither does it need to be.
The legislation dealing with this is
The Health Protection (Coronavirus, International Travel and Operator Liability) (England) Regulations 2021
Part 2, 3, confirms the legal obligations of those arriving in the U.K.
Part 3, 11, confirms the offence relating to the above.
a)without reasonable excuse P contravenes a requirement in regulation 3 (requirement to provide information);
Your “I would very much prefer not to fill in such a form and especially not to provide information which I consider to be private” is not a reasonable excuse.
You do however, have a choice.
You can provide the legally required information and abide by the law.
You can refuse to do so or give false information, in which case if you are found out, then the authorities will know where you will be for up to the next 10 years as the6 can impose a prison sentence to that maximum limit, and or a fine of £10000.
The final option of course is not to enter the U.K. until such information is no longer a legal requirement.