Could be a steatoda sp. Could be zygiella sp. hard to tell.
Neither are likely to do any harm, neither can bite particularly easily, their fangs are at the wrong angle for biting the relatively large, flat, tough targets a human body part presents, nor do they really want to except to save their own lives when squished.
You really can safely shoo out any UK spider.
If you find anything wandering about in newly purchased veg/fruit - theres a fb group, British Spider Identification and they will take the spider (you'll have to pop it in a tub and someone can collect or some can be posted) - this is helpful as it lets us learn more about what is being accidentally imported (again very very rarely anything risky!).
Unless you see the spider perform the bite, there is no way to determine a bite wound to a specific species or family - and any small puncture wound where something is injected, is a minor risk to health - good wound care and not dismissing small wounds because of their size will increase safety more than killing spiders would (mostly because most of the things that can and will bite you much more readily than a spider and are much more liable to transmit disease, are also the things spiders eat!).
Unless a health care person is also a spider expert and sees the spider, they also cannot diagnose a spider bite from a mosquito, horsefly, flea etc etc bite. No matter how confidently they state otherwise - a medical qualification does not remove someones ability to spout bullshit.