Yes as Robert says there should be VAT on recharged expenses.
If you think about it if he bought some materials for £100+VAT they would have cost him £120 but he would have claimed £20 VAT and have a cost of sale of £100. If he then charged the materials at no gain or loss he would recharge these at £100. If he didnt add VAT then he would be £20 up as this is what he has reclaimed from HMRC. That is why VAT would be chargeable so the recharge of the materials on a no gain/no loss basis from a profit and loss account viewpoint is also VAT neutral ie £20 VAT to be paid over when recharged.