What is the kind of this wasp killing spider from UK?
Hanging upside-down in a web suggests one of several groups, but in a building structure, and in what appears to be a messy, tangled web, I think we can safely put this one down as a member of the 'cobweb spiders' - the Theridiidae.  This group includes the infamous Black Widows, and some are known to successfully take relatively large and dangerous prey.
So, your particular spider has an obvious clue - the somewhat flattened dark abdomen with a large, light-colored patch in the middle of it.  The shape suggests Steatoda, and there is only one spider that this could be:  Steatoda nobilis, one of several spiders that frequently get called "False Widows".
Here are two links and a representative photo:
https://www.naturespot.org.uk/species/steatoda-nobilis
https://www.cabi.org/isc/datasheet/119917



Oh, I should add that despite the breathless hype the tabloids like to get up to, these spiders are known to be pretty harmless to people.  On rare occasions, a bite (which is not easy to get from these shy spiders) may produce symptoms like a mild Widow bite, but the discomfort seems to pass within a day or so.