Will try to be concise here and not drip-feed.
Few yrs ago friend who I had recently fallen out with got her son into school my DS went to (not same yr) by lying about her address. I had always been very vocal that I thought this was wrong.
Someone (later found out it was another friend who failed to get her DC in the previous yr and had moved away) wrote to admissions and grassed first friend up. School place was withdrawn.
Friend automatically assumed it was me, wrote me really nasty message through FB and deleted me. We have never spoken since as I deliberated and thought if she thinks that I would do that, then after several yrs of friendship she doesn't know me v well and I decided I didn't really want someone like that in my life. Admissions will not "eliminate" you from being in the frame as the author as people can then use a process of elimination to find out who it is.
She told her kids it was me which caused problems at school and her DS being really mean to my DS for several yrs which now seems to have died down (we both have sevral DC's who all cross paths at various schools)
Thing is I saw her DS the other day (the one who has the school place withdrawn) who gave me and DD evils at the local shops, I was very fond of him and it made me feel really sad that he thinks that I would hurt him like that and the same happened to DD yday when she saw ex friend and another of her DS's in town.
Just went to my local supermarket and they were there again giving me evils and I was worrying as I walked into each ailse that we would see them again and its so awkward, uncomfotable and unpleasant. I am crap with confrontation and don't really feel its appropraite to approach her in that situation or in front of the DC's.
I went to the pub on my b'day and was introduced to a lady who (unbeknowns to me) was a friend of this ex friend and when she realised who I was was really short with me and moved to another table.
Do I just do nothing and allow this person to continue to tell people lies about me or should I write her a letter just saying that it wasn't me and I'd appreciate it if she stopped telling people it was (surprises me as she doesn't look that great in the situation either tbh).
Its really beginning to make me :( and 
for me but mainly for my DC's we live around the corner from each other and atm seem to be crossing paths all the time.