The issues of aligning an aircraft with a curved, banked runway are very difficult. That's for a single aircraft with no additional traffic. Add a strong wind, and the difficulties of putting the aircraft on the ground at a predictable, consistently-achievable position, become severe. Yes, an extremely skilled, specially trained test pilot could achieve it, but it makes landing very much more difficult than it is now.
To exceed the benefits of a current dual-runway setup, this consistency must be achieved with an arrival rate of <40 seconds per movement, while simultaneously allowing departures at a similar rate. Those arrivals and departure need to follow set paths. That's fairly easy to achieve when the landing/take-off direction is constant and unmoving, but different landing and take-off performance coupled with variably-skilled pilots means that -particularly for take-off, the vector of each aircraft will be different. Equally, the amount of runway allocated for each movement must be sufficient to allow for all eventualities. The 2.5 mile length of Heathrow's runways does not include the extra ~half a mile or so of 'clearway', which is the fudge factor for upsets like the BA 777 a few years ago. However, the problem of providing a curvature and banking that the average pilot could cope with would, in my opinion, require a 'runway' of several miles diameter - using much more space than any current UK airport.