Supply teacher agency withdrawing furlough payment suddenly and claiming over payment

AP1109

I have been registered with the same supply teaching agency for a few years. Due to other contracts I only worked 2 days for them in the 2019/2020 tax year (March  19th+20th) and would have continued to support that particular secondary school due to significant staff shortage had they not closed due to COVID lockdown measures.
On April 16 2020 the agency informed me I would be furloughed and sent projected amounts for Mar / Apr / May.
I was sent a calculation sheet showing my yearly earnings as @ £255 - my daily rate being £127/day.
Their calculation table showed a daily rate of £43 and forward projection of furlough payment based on the number of furlough days in the month x £43 
I rcvd Mar/Apr payment, but I rcvd nothing in May - other than a refund of holiday pay wrongly taken from my furlough payment.
Endless phone calls yesterday being bounced between the education team and payroll - both of which denied it was their responsibility to explain or sort - resulted in me being told I had been "overpaid"
that I  "wasn't entitled to any payment anyway"
that "I had already been told about this" and that the monies already paid were not going to be reclaimed out of "goodwill"
I suspect the real reason I wont be asked to payback is because the agency have already made a claim from HMRC and will themselves be in trouble for miscalculation.
There was no explanation as to the reasoning behind any of this - or what I should now do other than demand a recalculation and professional explanation.
I a concerned I have accepted furlough payments fraudulently and will be liable to HMRC in the future.
As a supply teacher of course I don't have a contract but I know I would have continued to work at the school had they not closed down.
If anyone can advise me on what I should do or how to challenge the agency I would appreciate it. I have absolutely no trust in the agency based on these latest events.