Even though you may act as an agent and submit clients VAT, it is down to your client to pay their VAT return to HMRC, this is not an agents responsibility, an agent merely prepares and submits on clients behalf.
As an agent, once you have prepared and submitted return online, you let your client know the VAT to pay.
You can either set them up via the HMRC site to pay their VAT by Direct debit or they direct pay via BACS to HMRC.
If they choose the DD method this will be taken on the 12th following deadline date. If not they need to arrange payment on the VAT due date ie, end of month.
You can set up a direct debit from the agent account if your client wishes you to do this (this is useful since you can't for PAYE - you can only set up a DD from their HMRC account).
If you set up the direct debit and are not authorised on their Bank mandate, you need to print the forms off the HMRC website and get them to sign it. You will be prompted to do so when you set up the direct debit.
For non direct debit , the deadline for payment is the same a submission, before midnight on 7th following after month end, but it must be cleared funds and RECEIVED by HMRC by then, so care with the different payment methods. See HMRC guidance on their website.
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Joanne
Winner of Bookkeeper of the Year 2015, 2016 & 2017
Thoughts are my own/not to be regarded as official advice,which should be sought from a suitably qualified Accountant.
You should check out answers with reference to the legal position