There is no nationwide prohibition on physical contact between teachers and children. But there are positive duties for child safeguarding which might result in a local policy that is more restrictive. The exact legal background is different depending on whether this is happening in England, Scotland, etc., or on whether it's a state or private school, but the net result is the same. For music tuition which takes place outside school, bodies such as the Independent Society of Musicians (the UK's main professional association for musicians and music teachers) will have their own policies for members.
For example, for state schools in England, the governors must "make arrangements for ensuring that their functions relating to the conduct of the school are exercised with a view to safeguarding and promoting the welfare of children who are pupils at the school" (Education Act 2002 s.175(2)). This is a bit of a mouthful, but the rough idea is that the school has to implement certain policies in the interests of the child, including protecting them from sexual abuse and grooming. The school has to take account of statutory guidance from the Department for Education. In addition, there are standards for teachers' conduct which are used to assess their performance, and include language around safeguarding duties as well as "proper and professional regard for the ethos, policies and practices of the school in which they teach".
Now, there is nothing here to say that a teacher can never make physical contact with a pupil. There are rules about how allegations of abuse are meant to be handled, as well as the general employment law around unfair dismissal, which would mean that accidentally touching a child ought not to result in immediate sacking. A particular school could decide that on balance, the appropriate policy is one of no physical contact at all, or they could be more nuanced (which is likely). Whatever policy they do have must be communicated to the teaching staff, who naturally are meant to follow it - although again, there are requirements of fairness on the employer as to how they handle noncompliance.
Given that overall framework, scenarios of accidental touching, or administering first aid, or breaking up a dangerous situation, are different from physical contact as part of normal instruction. Even a local policy which ostensibly says "no touching ever" would have to give way to the Education and Inspections Act 2006, s.93 which specifically authorises our hypothetical teacher at an English state school to use reasonable force to stop a pupil injuring someone else, among other examples. That is also in line with the teachers' duty of care towards the wellbeing of their pupils. These examples are not really the same as what is happening in an ordinary music lesson.
Meanwhile, outside the school gates, the Independent Society of Musicans has its own Code of Conduct which includes specific rules about touching in Annex 2, paragraph 20.
Physical contact between teachers and pupils is only appropriate in very limited circumstances. Teachers should consider using other strategies such as demonstrating for the student to copy or using a mirror. If a teacher intends to use any physical contact in their teaching, they should state this in writing before lessons begin and ask the parent or guardian to sign that they have read the document. Explain the type of touch involved, where on the body and why, and make sure the pupil is aware of the reason for physical contact. Explain this orally to parents, guardians and pupils, and keep them informed of any need to modify the type of touch required as pupils progress. It is not advisable to touch a child on the trunk of the body unless there is a justifiable reason (e.g. to administer first aid). It is not appropriate to touch a child around the chest, waist, diaphragm or ribs in order to teach breathing.
These rules are also made in the context of safeguarding, with the threat of terminating ISM membership (at least in principle). Note that this does not say that touch is disallowed, but does ask it to be limited and respectful, and clearly signalled to the child and their parents or guardians. Other professional societies may well have their own rules.
All of this is happening at the level of law and policy, and so it's a little removed from the highly emotive social question of what sorts of behaviour are considered acceptable. Someone who teaches music in the UK would be exposed to a range of strongly-held views on the topic, which don't necessarily relate very clearly to the legal minimum requirements.