Rescheduling becomes confusing when several possible times look like confirmed lessons. Make the difference explicit.
Offer concrete choices
Instead of “Could we do later?”, try: “I can offer Wednesday 14 October at 16:30 or Thursday 15 October at 17:00, both UK time. Please confirm which works.” These dates are an example; use the actual dates you intend.
Confirm the final arrangement
Once agreed, state the original lesson and replacement together: “Our Tuesday lesson will move to Thursday at 17:00 for this week only.” Check whether the change affects one occurrence or the ongoing arrangement before editing the calendar.
Keep a single clear record
Update the schedule to match the agreement, and retain enough context to understand the change. If a proposal remains pending, say so. Do not let a conversational “maybe” become an apparently settled lesson.

Keep musical continuity
Add one short bridge: “Continue bars 1–2 until we meet; we will revisit the left-hand entry on Thursday.” This stops a changed date from leaving the learner without direction.
Your cancellation and replacement arrangements should be agreed with families. A message about a new time should not quietly introduce a new charge.