I've just put two new Goodyear "summer" tyres on the back of my E60 (replaced exactly the same tyres) and I can happily report that, even in the recent deluge of water I can once again plant my foot and get away from a junction with almost no flicker from the traction control.
I was at the point of nearly drifting out of junctions previously, tread was down at ~ 2mm on each tyre.
So my personal advice would be, in the majority of UK conditions summer tyres will be absolutely fine for normal driving, of far more importance is the amount of tread depth left and of course the quality of the tyre itself.
Saying that, nothing to suggest a winter tyre won't be better in those 2 days of snow that we probably won't get this year (and I won't leave the house for due to the fantastic nature of flexible home working), though I suspect at the cost of tyre noise/comfort/longevity/economy.