Ok so 3 months ago I was overpaid by my temping agency I was due to receive ￡93 before tax and ended up receiving ￡450, I did not notice as it was only a part time job and i did not really keep track of wages from that employer just on my regular wages.

Now they have pointed out the matter to me and are demanding I pay it all back, they have already with held ￡90 out of my weekly wage and are still demanding ￡300, but my argument is that I paid ￡130 tax more than I should of as the overpayment was a lot more than my regular wage and as they have admitted it was there mistake I don't see why I should have to pay back the money that was paid to the tax man and not me

I am willing to pay the difference of ￡170 in 2 instalments but can they make me pay back the additional ￡130 that the tax man took any help would be appreciated

They will fix the tax issue. Do not worry about that. It is not your money. You have to pay it back, immediately, if you can. If you quit and do not pay it back, expect criminal charges to be laid against you and you will still have to pay it back, and then some.

The tax will be automatically corrected because of the way PAYE works.

No one would believe that you did not notice being overpaid ￡450 just for a part time job. That is 2 whole weeks wages for me.

HMRC will have the overpaid tax so give them a call. The employer made the payment of tax on your behalf, they don't have it. You still need to repay them and recover the overpaid tax. As another answer says it will be automatically corrected but you can make it quicker if you phone HMRC.

you have to pay attention to your paycheck EVERY WEEK so this kind of thing doesn't happen or get worse

You have no choice. You have to pay it all back. this was unearned money, it was not yours.