Your client is trying to pull a fast one on you. This is one of the oldest tricks in the book. If they were aware of any confusion on your part, in your original quotation, regarding VAT, say if you failed to mention that the quote was ex-VAT, they are taking advantage of this.
It is usually a "given" in business that all cost prices, fees etc. are quoted ex-vat. As it is Revenue money at the end of the day and is not part of the sellers profit or the buyers cost.
If it is not too late insist that your quotation was ex-VAT or re-quote to include the 21.5% VAT otherwise you will be down the VAT content, your client will be up and Revenue get theirs anyway.