Extrapolation of Sinkewicz et al looking at coronary admissions due to stings. Work done by Professor Kounis and others on Kounis syndrome both frank and silent.
Mast cell mediated heart attacks caused by innate activation and degranulation by wasp toxins through toll like receptors as opposed to allergically mediated stimulation of high affinity receptors means that heart attacks from wasp stings go largely undiagnosed not least because of their delayed nature. This is recognised in the literature and to be honest paramedics and A&E crews don't go looking for wasp sting causality because they are too busy trying to save the patient.
Circa 5000 is down to a host of sources most of which are plauged by the paucity of causal reporting in the NHS. Cellulitis is recorded as cellulitis as opposed to wasp sting induced cellulitis etc. Just fortunate enough to have colleagues working at the coal face who have reported wasp sting admissions and extrapolating their experience provides a useful indication as to the extent of the problem.
The 200,000 to 400,000 comes from another host of sources including dozens of visitor attraction incident books. If one theme park reports 2000 first aid centre visits and 6 anaphylaxis cases based on 400,000 visitors over the said period, it's easy to see how that ramps up to 200,000 to 400,000 per annum and circa 1000 admissions for anaphylaxis.
Bear in mind that anaphylaxis only accounts for a minor proportion of hospital admissions for wasp stings but because of the immediacy and serious nature of anaphylaxis it gets attributed and reported more accurately.