The estate bears the cost, not the executor personally. A properly incurred valuation fee is ordinarily paid from estate funds, and where an executor pays first, the payment and reimbursement should be recorded in the estate accounts.
Valuation fees are not deductible for Inheritance Tax. HMRC's IHT400 notes state that fees incurred in dealing with the estate, including fees for valuing assets, cannot be deducted when calculating Inheritance Tax.
What does move the tax figure is the valuation basis. Open Market Value at the date of death is usually well below an insurance replacement figure, so using the correct basis — rather than copying across an old insurance valuation — is what keeps the estate from being overstated.
For estate-specific tax or accounting advice, speak to a probate solicitor, accountant or tax adviser.