Good for you. However, people do get bitten in the UK and some bites can be serious enough to require medical attention. This is something that self-evidently should be avoided if possible.
A friend of mine was bitten by a spider right here in the UK and it required treatment at A&E as the bite worsened rapidly after she was bitten. (N.B. I am not passing on any kind of urban legend; I saw the bite and I saw it rapidly developing throughout the day.)
Despite the fact that such bites are rare and (eventually) medically relatively minor, it is nevertheless incorrect to claim that there is no real cause for concern. The fact is that in the real world (in the UK at least), there is some cause for caution. It is sensible to take some level of avoiding action.
Despite having said all this, I strongly agree with you that we need spiders and that they should be treated with respect where feasible. Definitely do not kill them unless it is genuinely necessary.
But... false widows (such as the Steatoda nobilis pictured by Artistmike above) are invasive species[1] and I think there is ecological justification for killing them on sight. This is nothing to do with their slightly venomous nature and all to do with their ecological status. I don't kill them on sight in my home as they seem to be good insect catchers but I think that the ecological justification for instant death is valid for these three or four species in the UK.
Footnote:-
1: False widows (Steatoda nobilis, Steatoda grossa, Steatoda bipunctata and Steatoda paykulliana are present in the UK) are species that have existed in the UK for only about a century but seem to be spreading northwards very fast, possibly at the expense of native spider species. It can be argued that almost all British animal species are 'invasive', having re-entered the UK following the end of the last ice age, but false widows are definitely new and invasive/non-native by any sensible measure.