I’m guessing the lower figure you quoted initially was the vat on the tools you bought whereas what you’ve claimed is an income tax repayment -totally different taxes. As for the validity of your claim, I suspect that hinges on whether you are required to provide your own tools as a part of your employment contract. If so then you can make an appropriate claim. See tools and exps and remember you can make claims for earlier years too possibly.
Word of warning, just because you have the repayment does not mean it won’t be checked by HMRC at a later date i.e. within the next 12 months so KEEP all the paperwork just in case. HMRC sometimes check claims before paying and sometimes after.
