This sounds like a request for a schedule of payments under Section 16 (I think, from memory) TMA 1970. HMRC are entitled to ask you for this information - they then match names/addresses with their records and check (a) that they have the individuals registered as self employed and (b) that those individuals' tax returns are likely to reflect income from all sources known to HMRC. If no to either point (or possibly other points too) then HMRC might enquire into those individuals' returns.
Now how do they have assumed that I use other teachers?
Perhaps by looking at your own tax returns (or that of your limited company if you do indeed trade through a limited company, or have you used the term incorrectly and you are in fact a sole trader or acting in partnership?) and seeing a figure relating to such workers? Or is the engagement of workers inferred from information on your website? Or is your turnover simply too high to be generated by one or two people? Or are your premises logically occupied by more than one or two workers? Any or all of these points could apply here.
and why write to this address?
They might have incomplete information. But what does it matter? The letter obviously got to the right person/place.
I have used other self employed teachers occasionally but I am not sure if they have paid their own taxes, as it is not my problem.
If the teachers are genuinely self employed whilst engaged by you (which can be questionable if they are working under your direction on your premises for a set daily or hourly rate) then it is indeed not your problem. But do please be sure of their status before you simply say "self employed teachers". Employment status is not a matter of choice; it is determined by the terms and conditions of the engagement.
How do I deal with this letter?
Comply.