Even if there are no grounds for a formal complaint, it may be worth kicking up a fuss. (This may be particularly useful if you have witnessed something where, because you were not directly affected, you feel reluctant to make a formal complaint, but you still feel unhappy about the way you have seen police officers behave.)
With a more minor complaint, such as when a police officer has been rude to you, an offer from a senior officer to deal with the matter informally should be considered seriously. A formal investigation is a long drawn-out process; it’s worth avoiding if you just want an officer told off.
You can write to your MP, without asking them to make a formal complaint.
You can write directly to your local chief constable (or Borough Commander if in London), describing the incident and asking such questions as ‘Is this normal practice?’. They have to answer such letters, which means somebody has to investigate what happened.