Hi William
I think you situation would be covered by:
https://www.gov.uk/guidance/using-outward-processing-to-process-or-repair-your-goodsThis says: "VAT is charged on the repair costs, plus outward and inward freight charges, plus duty, but excluding insurance charges."
In this case no VAT should be charged at source ... but clearly you'd have to check that your Hungarian company is fine with that.
I haven't found anything on getting charged on any 'value of improvement' which would seem somewhat subjective for a lot of cases anyway.