Noise complaint to neighbouring shop: I am thinking to make it more legal.
Short Answer: dial 100 and make a complaint to the police.
Long Answer: Public nuisance of this sort can be both a tort and a criminal offence, each with their own legal remedies:
Section 91 of the Code of Civil Procedure allows for a suit to be brought for an injuction or any other suitable remedy but it does come with some caveats:
(1) in the case of a public nuisance or other wrongful act affecting,
or likely to affect, the public, a suit for a declaration and
injunction or for such other relief as may be appropriate in the
circumstances of the case, may be instituted,-
(a) by the Advocate General, or
(b) with the leave of the Court, by two or more persons, even though no special damage has been caused to such persons by reason of such
public nuisance or other wrongful act.
(2) Nothing in this section shall be deemed to limit or otherwise
affect any right of suit which may exist independently of its
provisions.
Subsection (2) does not prevent the complainant from seeking remedy under criminal law as well as damages under tort law.
Making a complaint to the police is potentially an easier route for remedy in the given circumstances.
Section 268 of the India Penal Code creates the offence of Public Nuisance:
A person is guilty of a public nuisance who does any act [...] which causes [...] annoyance to the public or to the people in general who dwell or occupy property in the vicinity, or which must necessarily cause [...] annoyance to persons who may have occasion to use any public right. A common nuisance is not excused on the ground that it causes some convenience or advantage.
The Magistrate, on receiving a police report may make an order under section 133 of the Criminal Procedure Code to stop, limit or regulate the nuisance. If the defendant objects, he may appear before the Magistrate to plead his case before final judgment is made:
(1) Whenever a District Magistrate [...], on receiving the report of a police officer or other information and on taking such evidence (if any) as he thinks fit, considers--
[...]
- (b) that the conduct of any trade or occupation, [...] is injurious to the [...] physical comfort of the community, and that in consequence such trade or occupation should be prohibited or regulated or such goods or merchandise should be removed or the keeping thereof regulated;
[...]
such Magistrate may make a conditional order requiring the person [...] carrying on such trade or occupation, or keeping any such goods or merchandise, [...] within a time to be fixed in the order--
[...]
- (ii) to desist from carrying on, or to remove or regulate in such manner as may be directed, such trade or occupation, or to remove such goods or merchandise, or to regulate the keeping thereof in such manner as may be directed;
[...]
or, if he (i.e. the person making the nuisance) objects so to do, to appear before himself or some other Executive Magistrate subordinate to him at a time and place to be fixed by the order, and show cause, in the manner hereinafter provided, why the order should not be made absolute.
(I've indicated with [...] where I have removed unnecessary words to make it relevant to the question and for ease of reading)