So are these readily available?
Sort of. They're not particularly rare, per se, but they have been out of print for many years now. Pricing tends to run low, under $5 a pack.
Here's two of the top hits for "playing cards bee bumblebee" from Google for buying the cards:
http://www.amazon.com/Bumble-Special-Generic-Quality-Playing/dp/B00B0YQK6Ihttps://www.kardwell.com/bee-bumble-bee.htmThe latter of the two, Kardwell, is the superior deal - they only sell by the brick, but they're a wholesaler - the per-deck cost is $2.50 for a mixed red/blue brick and gets lower when buying in larger quantities. I've bought from Kardwell before - it's hard to beat their pricing. Assuming you're in the UK, though, be prepared for Customs to charge fees your delivery - like I said, the company is a wholesaler so UK Customs probably know about them and may assume you're buying with the intent to sell at retail. Check into what the duties are before ordering.
However, if you only want a couple of packs, the former listing, from "Stay At Home Dads, We Know Games!!!" via Amazon, offers them in 2-deck pairs of red and blue - but with a high shipping/handling charge, probably higher still for you if you're located in London, assuming they'll even ship that far. SATDWKG always offers somewhat decent prices but with S/H charges that blows any savings you may have had out of the water.
If you're looking for a quality deck at this level that's good for magic, look for Richard Turner Gold Seal Bicycles. They're made on Bee Casino stock and traditionally cut. Typically they're about $4-$5 a pack at retail despite being out of print and can be identified by the classic box style (similar to the present "Bicycle 807" deck offered by shopbicyclecards.com) and a gold sticker on the back of the box which reads "Traditionally Cut for the Professional." Same quality as the Bumblebees but in the Bicycle Rider Back design, which has more gaff decks/cards than pretty much all other deck designs combined. They're generally carried only by magic shops or card speciality retailers.
Turner also ordered made some Bees of the same quality as well as his own brand, Gamblers, made with Bee faces and Bee Casino stock, but they're older and more scarce/expensive. If you're not familiar with the name, look him up - he's one of the finest card magicians alive today, despite being legally blind! If he ever lectures near you, GO!