If the UK has the primary rights to tax under treaty then HMRC are not going to allow an FTC under unilateral relief as legislation expressly restricts this.
If the client can't get an an exemption from withholding in Italy then HMRC would assume a tax refund in Italy would be filed instead to claim a refund under the terms of the double tax treaty. If the Italian authorities reject this then it would make interesting reading as to why. In addition, an FTC claim is usually based on the actual tax liability and not withholding taxes (although the latter is usually used as an estimate if the tax return in the other state has not yet been finalised in time, with the expectation that an amendment is made later if the difference is 'excessive').
sorry what is an FTC claim?